the 14 isometry classes of irreducible [6,2,5]_27 codes are:

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

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

code no       3:
================
1 1 1 1 2 0
9 3 2 1 0 2
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 }

code no       4:
================
1 1 1 1 2 0
11 3 2 1 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 25 0 0 
4 0 0 0 
0 0 0 24 
0 0 12 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(3, 4)(5, 6)
orbits: { 1, 2 }, { 3, 4 }, { 5, 6 }

code no       5:
================
1 1 1 1 2 0
18 3 2 1 0 2
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 }

code no       6:
================
1 1 1 1 2 0
19 3 2 1 0 2
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
17 4 10 20 
22 22 22 22 
0 0 0 24 
0 0 7 0 
, 0
, 
16 16 16 16 
5 23 21 15 
0 0 0 17 
0 0 2 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 6)(2, 5)(3, 4), 
(1, 5)(2, 6)(3, 4)
orbits: { 1, 6, 5, 2 }, { 3, 4 }

code no       7:
================
1 1 1 1 2 0
9 4 3 1 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 23 0 0 
4 0 0 0 
22 3 26 16 
13 13 13 13 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(3, 6)(4, 5)
orbits: { 1, 2 }, { 3, 6 }, { 4, 5 }

code no       8:
================
1 1 1 1 2 0
10 4 3 1 0 2
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 }

code no       9:
================
1 1 1 1 2 0
12 4 3 1 0 2
the automorphism group has order 6
and is strongly generated by the following 2 elements:
(
5 5 5 5 
0 0 0 16 
19 25 7 18 
0 9 0 0 
, 0
, 
19 25 7 18 
6 0 0 0 
14 14 14 14 
0 0 18 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 5)(2, 4)(3, 6), 
(1, 2, 6)(3, 4, 5)
orbits: { 1, 5, 6, 4, 3, 2 }

code no      10:
================
1 1 1 1 2 0
14 4 3 1 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 22 
15 9 22 26 
18 18 18 18 
3 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 4)(2, 6)(3, 5)
orbits: { 1, 4 }, { 2, 6 }, { 3, 5 }

code no      11:
================
1 1 1 1 2 0
16 4 3 1 0 2
the automorphism group has order 6
and is strongly generated by the following 2 elements:
(
0 0 17 0 
0 0 0 12 
10 10 10 10 
4 20 12 17 
, 2
, 
0 0 0 11 
0 0 16 0 
9 3 5 1 
18 18 18 18 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(1, 5, 3)(2, 6, 4), 
(1, 6, 3, 2, 5, 4)
orbits: { 1, 3, 4, 5, 6, 2 }

code no      12:
================
1 1 1 1 2 0
10 7 3 1 0 2
the automorphism group has order 6
and is strongly generated by the following 1 elements:
(
0 0 0 13 
1 17 9 26 
0 22 0 0 
0 0 18 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(1, 5, 6, 2, 3, 4)
orbits: { 1, 4, 3, 2, 6, 5 }

code no      13:
================
1 1 1 1 2 0
11 7 3 1 0 2
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 10 
13 13 13 13 
15 20 26 16 
11 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 4)(2, 5)(3, 6)
orbits: { 1, 4 }, { 2, 5 }, { 3, 6 }

code no      14:
================
1 1 1 1 2 0
20 17 3 1 0 2
the automorphism group has order 18
and is strongly generated by the following 3 elements:
(
1 0 0 0 
6 14 26 7 
0 0 11 0 
0 23 0 0 
, 2
, 
0 0 19 0 
0 19 0 0 
11 11 11 11 
0 0 0 19 
, 2
, 
22 26 2 11 
17 17 17 17 
0 0 0 14 
0 0 23 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 4, 6), 
(1, 5, 3), 
(1, 6)(2, 5)(3, 4)
orbits: { 1, 3, 6, 5, 4, 2 }