the 7 isometry classes of irreducible [5,2,4]_25 codes are:

code no       1:
================
1 1 1 4 0
3 2 1 0 4
the automorphism group has order 40
and is strongly generated by the following 5 elements:
(
7 0 0 
0 7 0 
0 0 7 
, 1
, 
8 0 0 
0 0 22 
11 11 11 
, 0
, 
18 18 18 
0 0 12 
0 12 0 
, 1
, 
0 24 0 
6 6 6 
24 0 0 
, 1
, 
23 7 16 
23 0 0 
0 14 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
id, 
(2, 5, 4, 3), 
(1, 4)(2, 3), 
(1, 3, 4, 2), 
(1, 2, 3, 5)
orbits: { 1, 4, 2, 5, 3 }

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

code no       3:
================
1 1 1 4 0
6 2 1 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
18 0 0 
0 0 21 
0 17 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(4, 5)
orbits: { 1 }, { 2, 3 }, { 4, 5 }

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

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

code no       6:
================
1 1 1 4 0
8 5 1 0 4
the automorphism group has order 4
and is strongly generated by the following 1 elements:
(
5 22 21 
0 0 1 
17 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(1, 3, 2, 5)
orbits: { 1, 5, 2, 3 }, { 4 }

code no       7:
================
1 1 1 4 0
17 6 1 0 4
the automorphism group has order 12
and is strongly generated by the following 4 elements:
(
22 0 0 
0 22 0 
8 8 8 
, 1
, 
7 0 0 
19 21 24 
9 9 9 
, 0
, 
7 7 7 
0 23 0 
0 0 23 
, 1
, 
0 0 15 
0 15 0 
10 10 10 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(3, 4), 
(2, 5)(3, 4), 
(1, 4), 
(1, 4, 3)
orbits: { 1, 4, 3 }, { 2, 5 }