the 1 isometry classes of irreducible [7,1,7]_5 codes are:

code no       1:
================
1 1 1 1 1 1 4
the automorphism group has order 5040
and is strongly generated by the following 10 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
4 4 4 4 4 4 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
0 0 0 0 1 0 
, 
2 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
0 0 0 2 0 0 
3 3 3 3 3 3 
0 0 0 0 2 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 0 0 1 
0 0 0 1 0 0 
0 0 0 0 1 0 
, 
4 0 0 0 0 0 
0 4 0 0 0 0 
0 0 4 0 0 0 
1 1 1 1 1 1 
0 0 0 0 0 4 
0 0 0 0 4 0 
, 
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 0 3 0 0 
0 0 3 0 0 0 
0 0 0 0 3 0 
0 0 0 0 0 3 
, 
2 0 0 0 0 0 
0 2 0 0 0 0 
3 3 3 3 3 3 
0 0 0 2 0 0 
0 0 0 0 2 0 
0 0 2 0 0 0 
, 
4 0 0 0 0 0 
0 0 4 0 0 0 
0 0 0 4 0 0 
0 0 0 0 0 4 
0 0 0 0 4 0 
0 4 0 0 0 0 
, 
0 0 0 1 0 0 
0 0 0 0 0 1 
1 0 0 0 0 0 
0 0 0 0 1 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
, 
3 3 3 3 3 3 
0 0 0 2 0 0 
0 2 0 0 0 0 
0 0 0 0 0 2 
0 0 0 0 2 0 
0 0 2 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(5, 6), 
(5, 6, 7), 
(4, 5, 6), 
(4, 7)(5, 6), 
(3, 4), 
(3, 6, 7), 
(2, 6, 4, 3), 
(1, 3, 5, 4)(2, 6), 
(1, 7)(2, 3, 6, 4)
orbits: { 1, 4, 7, 6, 3, 5, 2 }