the 14 isometry classes of irreducible [14,6,7]_4 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
3 1 3 3 1 0 0 1 0 0 0 1 0 0
2 1 3 0 0 1 2 1 0 0 0 0 1 0
2 2 0 1 0 3 3 1 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
1 0 0 0 0 0 0 0 
2 2 0 3 0 1 1 3 
0 0 0 1 0 0 0 0 
0 0 1 0 0 0 0 0 
1 2 3 0 0 2 1 2 
1 3 1 1 3 0 0 3 
3 3 3 3 3 3 3 3 
0 0 0 0 0 0 0 1 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 14)(3, 4)(5, 13)(6, 12)(7, 9)(10, 11)
orbits: { 1 }, { 2, 14 }, { 3, 4 }, { 5, 13 }, { 6, 12 }, { 7, 9 }, { 8 }, { 10, 11 }

code no       2:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
3 1 3 3 1 0 0 1 0 0 0 1 0 0
3 2 1 3 2 3 2 1 0 0 0 0 1 0
3 1 2 0 0 2 3 1 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 2 0 0 0 0 0 0 
3 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 0 2 0 0 0 
0 0 0 3 0 0 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 0 3 0 0 
0 0 0 0 0 0 0 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(4, 5)(6, 7)(9, 13)(10, 11)
orbits: { 1, 2 }, { 3 }, { 4, 5 }, { 6, 7 }, { 8 }, { 9, 13 }, { 10, 11 }, { 12 }, { 14 }

code no       3:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
3 1 3 3 1 0 0 1 0 0 0 1 0 0
3 2 1 3 2 3 2 1 0 0 0 0 1 0
2 3 1 1 2 2 3 1 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 2 0 0 0 0 0 0 
3 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 0 2 0 0 0 
0 0 0 3 0 0 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 0 3 0 0 
0 0 0 0 0 0 0 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(4, 5)(6, 7)(9, 13)(10, 11)
orbits: { 1, 2 }, { 3 }, { 4, 5 }, { 6, 7 }, { 8 }, { 9, 13 }, { 10, 11 }, { 12 }, { 14 }

code no       4:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
2 3 1 1 2 0 0 1 0 0 0 1 0 0
2 2 1 0 0 2 1 1 0 0 0 0 1 0
3 2 0 1 0 1 2 1 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 0 0 0 0 1 
2 2 2 1 1 1 0 0 
0 0 3 0 0 0 0 0 
3 1 2 2 3 0 0 2 
0 0 0 0 0 2 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 0 3 0 
2 0 0 0 0 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 8)(2, 10)(4, 12)(5, 6)(13, 14)
orbits: { 1, 8 }, { 2, 10 }, { 3 }, { 4, 12 }, { 5, 6 }, { 7 }, { 9 }, { 11 }, { 13, 14 }

code no       5:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
2 3 1 1 2 0 0 1 0 0 0 1 0 0
1 2 3 2 0 2 1 1 0 0 0 0 1 0
0 2 2 3 0 1 2 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 3 
0 1 1 3 0 2 1 2 
2 1 3 1 0 1 2 2 
0 3 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 
3 3 3 3 3 3 3 3 
, 1
, 
3 1 2 2 3 0 0 2 
0 0 0 0 0 0 2 0 
0 0 2 0 0 0 0 0 
0 0 0 0 0 0 0 3 
2 1 3 1 3 0 3 0 
0 0 0 0 0 2 0 0 
0 2 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 5, 9, 8)(3, 6, 10, 14)(4, 7, 11, 13), 
(1, 12)(2, 7)(4, 8)(5, 11)(9, 13)
orbits: { 1, 12 }, { 2, 8, 7, 9, 4, 5, 13, 11 }, { 3, 14, 10, 6 }

code no       6:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
2 3 1 1 2 0 0 1 0 0 0 1 0 0
1 2 3 2 0 2 1 1 0 0 0 0 1 0
3 0 0 1 2 3 3 1 0 0 0 0 0 1
the automorphism group has order 6
and is strongly generated by the following 2 elements:
(
3 0 0 0 0 0 0 0 
0 0 0 0 0 0 2 0 
0 0 3 0 0 0 0 0 
0 0 0 3 0 0 0 0 
2 1 3 1 3 0 3 0 
0 0 0 0 0 0 0 2 
0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 
, 0
, 
3 1 2 2 3 0 0 2 
0 0 0 0 0 0 2 0 
0 0 2 0 0 0 0 0 
0 0 0 0 0 0 0 3 
2 1 3 1 3 0 3 0 
0 0 0 0 0 2 0 0 
0 2 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 7)(5, 11)(6, 8)(9, 14)(10, 12), 
(1, 12)(2, 7)(4, 8)(5, 11)(9, 13)
orbits: { 1, 12, 10 }, { 2, 7 }, { 3 }, { 4, 8, 6 }, { 5, 11 }, { 9, 14, 13 }

code no       7:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
3 1 2 1 2 0 0 1 0 0 0 1 0 0
3 0 0 3 3 1 1 1 0 0 0 0 1 0
3 0 3 1 0 3 2 1 0 0 0 0 0 1
the automorphism group has order 12
and is strongly generated by the following 2 elements:
(
3 0 0 0 0 0 0 0 
0 0 0 0 0 0 3 0 
2 1 3 1 3 0 3 0 
0 0 0 0 0 0 0 3 
2 3 1 3 1 0 0 3 
0 0 0 1 0 0 0 0 
2 2 2 2 2 2 2 2 
1 0 0 1 1 2 2 2 
, 0
, 
1 0 0 0 0 0 0 0 
0 0 0 3 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 0 0 3 0 0 0 
0 0 3 0 0 0 0 0 
2 1 3 1 3 0 0 1 
0 0 0 0 0 1 0 0 
1 1 1 1 1 1 1 1 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 10, 12, 5, 9, 7)(3, 13, 8, 4, 6, 11), 
(2, 3, 5, 4)(6, 7, 13, 12)(8, 10, 11, 9)
orbits: { 1 }, { 2, 7, 4, 9, 6, 8, 5, 11, 12, 13, 3, 10 }, { 14 }

code no       8:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
3 1 2 1 2 0 0 1 0 0 0 1 0 0
3 0 0 3 3 1 1 1 0 0 0 0 1 0
0 1 0 2 1 3 2 1 0 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 3 elements:
(
2 0 0 0 0 0 0 0 
3 0 0 3 3 1 1 1 
2 2 2 1 1 1 0 0 
1 1 1 1 1 1 1 1 
0 0 0 0 0 1 0 0 
2 1 3 1 3 0 3 0 
0 0 0 2 0 0 0 0 
0 2 0 0 0 0 0 0 
, 0
, 
2 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 
2 3 1 3 1 0 1 0 
2 1 3 1 3 0 0 1 
2 2 2 3 3 3 0 0 
0 0 0 0 1 0 0 0 
0 0 0 1 0 0 0 0 
, 1
, 
0 3 0 1 3 2 1 3 
0 0 0 0 0 2 0 0 
0 0 0 0 0 0 1 0 
3 1 2 1 2 0 0 1 
1 0 0 1 1 2 2 2 
0 2 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
1 3 2 3 2 0 2 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 8, 13)(3, 12, 10)(4, 7, 9)(5, 11, 6), 
(2, 12, 5, 7)(3, 11, 4, 8)(6, 9, 13, 10), 
(1, 14)(2, 6)(3, 7)(4, 12)(5, 13)(8, 11)(9, 10)
orbits: { 1, 14 }, { 2, 13, 7, 6, 8, 9, 5, 4, 3, 11, 10, 12 }

code no       9:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
3 3 2 1 3 0 0 1 0 0 0 1 0 0
2 0 3 3 2 3 2 1 0 0 0 0 1 0
2 3 0 0 1 2 3 1 0 0 0 0 0 1
the automorphism group has order 6
and is strongly generated by the following 2 elements:
(
0 0 0 2 0 0 0 0 
1 1 3 2 1 0 0 2 
0 0 3 0 0 0 0 0 
1 1 1 1 1 1 1 1 
0 0 0 0 0 0 2 0 
3 0 1 1 3 1 3 2 
0 0 0 0 0 0 0 1 
0 0 0 0 3 0 0 0 
, 0
, 
1 1 3 2 1 0 0 2 
0 0 0 1 0 0 0 0 
2 3 0 0 1 2 3 1 
0 2 0 0 0 0 0 0 
0 0 0 0 0 2 0 0 
0 0 0 0 1 0 0 0 
1 3 2 3 2 0 2 0 
1 0 2 2 1 2 1 3 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 9, 4)(2, 10, 12)(5, 8, 7)(6, 11, 13), 
(1, 12)(2, 4)(3, 14)(5, 6)(7, 11)(8, 13)(9, 10)
orbits: { 1, 4, 12, 9, 2, 10 }, { 3, 14 }, { 5, 7, 6, 8, 11, 13 }

code no      10:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
2 3 2 2 3 0 0 1 0 0 0 1 0 0
3 1 2 2 2 3 1 1 0 0 0 0 1 0
0 1 1 2 3 2 2 1 0 0 0 0 0 1
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }, { 11 }, { 12 }, { 13 }, { 14 }

code no      11:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
2 3 2 2 3 0 0 1 0 0 0 1 0 0
0 0 3 1 3 3 1 1 0 0 0 0 1 0
0 3 3 0 1 2 3 1 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
2 1 3 1 3 0 3 0 
0 0 0 3 0 0 0 0 
2 2 2 2 2 2 2 2 
0 3 0 0 0 0 0 0 
0 0 0 0 0 2 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 2 
0 0 0 0 0 0 1 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 11)(2, 4)(3, 9)(5, 6)(7, 8)(10, 14)(12, 13)
orbits: { 1, 11 }, { 2, 4 }, { 3, 9 }, { 5, 6 }, { 7, 8 }, { 10, 14 }, { 12, 13 }

code no      12:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
2 3 2 2 3 0 0 1 0 0 0 1 0 0
0 1 1 2 3 2 2 1 0 0 0 0 1 0
2 0 1 0 3 1 3 1 0 0 0 0 0 1
the automorphism group has order 14
and is strongly generated by the following 2 elements:
(
3 2 1 2 1 0 1 0 
0 2 2 3 1 3 3 2 
0 0 0 0 0 0 0 3 
1 1 1 3 3 3 0 0 
0 0 2 0 0 0 0 0 
1 0 3 0 2 3 2 3 
0 0 0 1 0 0 0 0 
0 0 0 0 0 3 0 0 
, 0
, 
0 1 0 0 0 0 0 0 
0 0 0 0 0 0 3 0 
3 3 3 3 3 3 3 3 
0 0 2 0 0 0 0 0 
3 3 3 1 1 1 0 0 
2 0 0 0 0 0 0 0 
0 0 0 0 3 0 0 0 
2 1 2 2 1 0 0 3 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(1, 12, 9, 10, 4, 7, 11)(2, 14, 6, 8, 3, 5, 13), 
(1, 6, 9, 3, 4, 13, 11, 14, 12, 8, 10, 5, 7, 2)
orbits: { 1, 11, 2, 7, 13, 4, 5, 10, 3, 9, 8, 12, 6, 14 }

code no      13:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
3 1 2 2 0 1 0 1 0 0 0 1 0 0
0 3 0 1 1 3 2 1 0 0 0 0 1 0
0 0 2 3 2 3 3 1 0 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 
, 0
, 
2 1 3 1 3 0 3 0 
2 2 2 1 1 1 0 0 
0 0 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 2 0 0 
0 0 0 0 3 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 1 
, 0
, 
0 0 3 0 0 0 0 0 
0 0 0 2 0 0 0 0 
0 0 0 0 0 0 2 0 
0 0 1 3 1 3 3 2 
0 0 0 0 0 3 0 0 
0 0 0 0 1 0 0 0 
3 3 3 3 3 3 3 3 
0 1 0 3 3 1 2 3 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(5, 6)(7, 8)(11, 12)(13, 14), 
(1, 11)(2, 10)(4, 7)(5, 6)(9, 13), 
(1, 13, 8, 10, 11, 14, 4, 2, 12, 9, 7, 3)(5, 6)
orbits: { 1, 11, 3, 12, 10, 2, 7, 8, 4, 9, 13, 14 }, { 5, 6 }

code no      14:
================
1 1 1 1 1 1 1 1 1 0 0 0 0 0
2 2 2 1 1 1 0 0 0 1 0 0 0 0
3 2 1 2 1 0 1 0 0 0 1 0 0 0
3 2 1 3 2 1 0 1 0 0 0 1 0 0
0 1 1 2 2 0 2 1 0 0 0 0 1 0
3 0 3 1 0 2 3 1 0 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 2 2 3 3 0 3 2 
3 3 3 2 2 2 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 
0 0 3 0 0 0 0 0 
1 0 1 2 0 3 1 2 
3 2 1 3 2 1 0 1 
0 0 0 3 0 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 13)(2, 10)(3, 5)(4, 8)(6, 14)(7, 12)(9, 11)
orbits: { 1, 13 }, { 2, 10 }, { 3, 5 }, { 4, 8 }, { 6, 14 }, { 7, 12 }, { 9, 11 }