the 2 isometry classes of irreducible [7,4,4]_8 codes are:

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

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