the 1 isometry classes of irreducible [7,3,4]_2 codes are:

code no       1:
================
1 1 1 0 1 0 0
1 1 0 1 0 1 0
1 0 1 1 0 0 1
the automorphism group has order 168
and is strongly generated by the following 7 elements:
(
1 0 0 0 
0 1 0 0 
1 1 1 0 
1 1 0 1 
, 
1 0 0 0 
0 1 0 0 
0 0 0 1 
0 0 1 0 
, 
1 0 0 0 
1 0 1 1 
0 0 0 1 
1 1 0 1 
, 
1 0 0 0 
0 0 1 0 
1 1 1 0 
1 0 1 1 
, 
1 1 1 0 
0 0 1 0 
0 1 0 0 
0 0 0 1 
, 
1 1 0 1 
0 0 0 1 
0 1 0 0 
0 0 1 0 
, 
1 0 1 1 
0 0 1 0 
1 1 0 1 
1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 6), 
(3, 4)(5, 6), 
(2, 7)(3, 5, 6, 4), 
(2, 5, 3)(4, 6, 7), 
(1, 5)(2, 3), 
(1, 5, 6)(2, 3, 4), 
(1, 4, 6, 3, 2, 5, 7)
orbits: { 1, 5, 6, 7, 3, 2, 4 }