the 16 isometry classes of irreducible [9,3,6]_5 codes are:

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

code no       2:
================
1 1 1 1 1 1 4 0 0
3 2 2 1 1 0 0 4 0
4 3 2 1 0 1 0 0 4
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 }

code no       3:
================
1 1 1 1 1 1 4 0 0
3 2 2 1 1 0 0 4 0
2 4 2 1 0 1 0 0 4
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 }

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

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

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

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

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

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

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

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

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

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

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

code no      15:
================
1 1 1 1 1 1 4 0 0
3 2 2 1 1 0 0 4 0
3 1 0 4 2 1 0 0 4
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
2 0 0 0 0 0 
0 0 2 0 0 0 
0 2 0 0 0 0 
0 0 0 0 2 0 
0 0 0 2 0 0 
3 3 3 3 3 3 
, 
4 1 1 3 3 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
0 0 0 0 0 4 
1 1 1 1 1 1 
0 0 0 1 0 0 
, 
0 0 0 0 0 4 
1 2 0 3 4 2 
0 3 0 0 0 0 
4 4 4 4 4 4 
4 1 1 3 3 0 
0 0 0 0 4 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(4, 5)(6, 7), 
(1, 8)(4, 6)(5, 7), 
(1, 7, 4, 8, 5, 6)(2, 3, 9)
orbits: { 1, 8, 6, 4, 7, 5 }, { 2, 3, 9 }

code no      16:
================
1 1 1 1 1 1 4 0 0
3 2 2 1 1 0 0 4 0
3 4 0 4 2 1 0 0 4
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 0 0 4 0 
1 4 4 2 2 0 
0 0 1 0 0 0 
0 0 0 0 0 3 
, 
4 1 1 3 3 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
0 0 0 0 0 4 
1 1 1 1 1 1 
0 0 0 1 0 0 
, 
0 0 0 3 0 0 
0 2 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
2 1 0 1 3 4 
3 2 2 1 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 8)(7, 9), 
(1, 8)(4, 6)(5, 7), 
(1, 8, 6, 4)(3, 7, 9, 5)
orbits: { 1, 8, 4, 6 }, { 2 }, { 3, 5, 7, 9 }