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

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