the 2 isometry classes of irreducible [7,2,4]_2 codes are:

code no       1:
================
1 1 1 1 1 1 0
1 1 1 0 0 0 1
the automorphism group has order 72
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
0 0 0 1 0 
0 0 0 0 1 
1 1 1 1 1 
0 1 0 0 0 
0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(4, 5), 
(2, 3), 
(1, 6, 3, 5, 2, 4)
orbits: { 1, 4, 5, 2, 6, 3 }, { 7 }

code no       2:
================
1 1 1 0 0 1 0
1 1 0 1 1 0 1
the automorphism group has order 48
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 0 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 0 1 1 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
0 1 0 0 0 
1 0 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 1 1 0 0 
0 0 1 0 0 
1 0 0 0 0 
0 0 0 0 1 
0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 7), 
(4, 5), 
(4, 7), 
(3, 6), 
(1, 2), 
(1, 3, 2, 6)(4, 5)
orbits: { 1, 2, 6, 3 }, { 4, 5, 7 }