the 2 isometry classes of irreducible [7,3,5]_8 codes are:

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

code no       2:
================
1 1 1 1 1 0 0
4 3 2 1 0 1 0
3 6 5 1 0 0 1
the automorphism group has order 42
and is strongly generated by the following 5 elements:
(
1 0 0 0 
0 0 0 6 
3 1 2 4 
2 2 2 2 
, 2
, 
7 0 0 0 
2 3 1 4 
0 1 0 0 
5 2 6 4 
, 1
, 
5 5 5 5 
0 0 0 1 
0 7 0 0 
0 0 3 0 
, 1
, 
0 2 0 0 
4 1 3 2 
3 3 3 3 
7 0 0 0 
, 1
, 
3 6 5 1 
6 4 3 7 
0 4 0 0 
6 6 6 6 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 5, 4)(3, 6, 7), 
(2, 3, 5, 6, 4, 7), 
(1, 6, 5)(2, 3, 4), 
(1, 4, 5, 3, 6, 2), 
(1, 5, 4, 6, 2, 3, 7)
orbits: { 1, 5, 2, 7, 3, 6, 4 }