the 3 isometry classes of irreducible [7,2,5]_5 codes are:

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

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

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