the 19 isometry classes of irreducible [6,2,5]_25 codes are:

code no       1:
================
1 1 1 1 4 0
4 3 2 1 0 4
the automorphism group has order 240
and is strongly generated by the following 7 elements:
(
24 0 0 0 
0 24 0 0 
0 0 24 0 
0 0 0 24 
, 1
, 
2 0 0 0 
0 3 0 0 
4 4 4 4 
4 3 2 1 
, 1
, 
16 0 0 0 
0 23 0 0 
0 0 0 7 
16 16 16 16 
, 0
, 
20 0 0 0 
5 5 5 5 
0 0 0 20 
0 0 20 0 
, 0
, 
12 0 0 0 
0 0 0 12 
0 12 0 0 
18 18 18 18 
, 0
, 
0 0 13 0 
0 0 0 13 
17 17 17 17 
13 0 0 0 
, 1
, 
1 2 3 4 
0 4 0 0 
0 0 0 2 
0 0 3 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(3, 5)(4, 6), 
(3, 6, 5, 4), 
(2, 5)(3, 4), 
(2, 3, 5, 4), 
(1, 4, 2, 5, 3), 
(1, 6)(3, 4)
orbits: { 1, 3, 6, 5, 4, 2 }

code no       2:
================
1 1 1 1 4 0
5 3 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
13 0 0 0 
0 14 0 0 
7 7 7 7 
10 14 16 23 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 6)
orbits: { 1 }, { 2 }, { 3, 5 }, { 4, 6 }

code no       3:
================
1 1 1 1 4 0
6 5 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
24 0 0 0 
0 11 0 0 
0 0 0 13 
0 0 21 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(5, 6)
orbits: { 1 }, { 2 }, { 3, 4 }, { 5, 6 }

code no       4:
================
1 1 1 1 4 0
7 5 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
4 12 17 21 
0 0 12 0 
0 17 0 0 
1 1 1 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 6)(2, 3)(4, 5)
orbits: { 1, 6 }, { 2, 3 }, { 4, 5 }

code no       5:
================
1 1 1 1 4 0
8 5 2 1 0 4
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
12 0 0 0 
0 22 0 0 
5 5 5 5 
13 3 15 20 
, 1
, 
0 12 0 0 
12 0 0 0 
18 18 18 18 
0 0 0 12 
, 1
, 
12 5 23 14 
0 0 0 21 
0 0 12 0 
23 0 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 6), 
(1, 2)(3, 5), 
(1, 4, 2, 6)
orbits: { 1, 2, 6, 4 }, { 3, 5 }

code no       6:
================
1 1 1 1 4 0
9 5 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
22 22 22 22 
1 8 14 7 
0 0 0 1 
0 0 24 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 5)(2, 6)(3, 4)
orbits: { 1, 5 }, { 2, 6 }, { 3, 4 }

code no       7:
================
1 1 1 1 4 0
12 5 2 1 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 }

code no       8:
================
1 1 1 1 4 0
19 5 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
9 0 0 0 
0 3 0 0 
0 0 0 20 
0 0 15 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(5, 6)
orbits: { 1 }, { 2 }, { 3, 4 }, { 5, 6 }

code no       9:
================
1 1 1 1 4 0
24 5 2 1 0 4
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
21 0 0 0 
0 7 0 0 
4 4 4 4 
5 24 2 1 
, 1
, 
14 0 0 0 
0 1 0 0 
0 0 0 15 
0 0 5 0 
, 1
, 
0 11 0 0 
11 0 0 0 
0 0 11 0 
0 0 0 11 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 6), 
(3, 4)(5, 6), 
(1, 2)
orbits: { 1, 2 }, { 3, 5, 4, 6 }

code no      10:
================
1 1 1 1 4 0
9 6 2 1 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 }

code no      11:
================
1 1 1 1 4 0
10 6 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 2 
1 1 1 1 
20 12 4 2 
9 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      12:
================
1 1 1 1 4 0
11 6 2 1 0 4
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
17 0 0 0 
0 16 0 0 
0 0 0 15 
0 0 5 0 
, 1
, 
0 20 0 0 
12 0 0 0 
4 16 11 8 
19 19 19 19 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(5, 6), 
(1, 2)(3, 6)(4, 5)
orbits: { 1, 2 }, { 3, 4, 6, 5 }

code no      13:
================
1 1 1 1 4 0
12 6 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 0 0 17 
0 0 9 0 
0 11 0 0 
22 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 4)(2, 3)(5, 6)
orbits: { 1, 4 }, { 2, 3 }, { 5, 6 }

code no      14:
================
1 1 1 1 4 0
13 6 2 1 0 4
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
0 15 0 0 
6 0 0 0 
0 0 3 0 
21 12 4 2 
, 0
, 
0 0 0 22 
3 15 16 23 
10 10 10 10 
17 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(4, 6), 
(1, 4)(2, 6)(3, 5)
orbits: { 1, 2, 4, 6 }, { 3, 5 }

code no      15:
================
1 1 1 1 4 0
19 6 2 1 0 4
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
22 0 0 0 
0 15 0 0 
0 0 0 2 
0 0 4 0 
, 1
, 
0 0 0 20 
5 5 5 5 
0 0 20 0 
20 0 0 0 
, 1
, 
0 8 0 0 
19 0 0 0 
21 7 10 5 
15 15 15 15 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(5, 6), 
(1, 4)(2, 5), 
(1, 2)(3, 6)(4, 5)
orbits: { 1, 4, 2, 3, 5, 6 }

code no      16:
================
1 1 1 1 4 0
20 6 2 1 0 4
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
11 0 0 0 
0 6 0 0 
0 0 0 17 
0 0 9 0 
, 1
, 
0 19 0 0 
19 0 0 0 
0 0 19 0 
0 0 0 19 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(5, 6), 
(1, 2)
orbits: { 1, 2 }, { 3, 4 }, { 5, 6 }

code no      17:
================
1 1 1 1 4 0
10 9 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 8 0 0 
6 0 0 0 
14 12 15 20 
10 10 10 10 
, 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      18:
================
1 1 1 1 4 0
23 9 2 1 0 4
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
21 0 0 0 
0 21 0 0 
9 9 9 9 
0 0 0 21 
, 1
, 
0 15 0 0 
15 0 0 0 
10 10 10 10 
0 0 0 15 
, 0
, 
7 7 7 7 
0 0 7 0 
0 24 0 0 
17 4 16 23 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 5), 
(1, 2)(3, 5), 
(1, 5)(2, 3)(4, 6)
orbits: { 1, 2, 5, 3 }, { 4, 6 }

code no      19:
================
1 1 1 1 4 0
13 6 5 1 0 4
the automorphism group has order 6
and is strongly generated by the following 2 elements:
(
0 0 20 0 
0 0 0 4 
17 0 0 0 
0 24 0 0 
, 0
, 
22 22 22 22 
0 0 20 0 
0 17 0 0 
10 16 13 8 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(1, 3)(2, 4)(5, 6), 
(1, 5)(2, 3)(4, 6)
orbits: { 1, 3, 5, 2, 6, 4 }