the 1 isometry classes of irreducible [8,4,4]_2 codes are:

code no       1:
================
1 1 1 0 1 0 0 0
1 1 0 1 0 1 0 0
1 0 1 1 0 0 1 0
0 1 1 1 0 0 0 1
the automorphism group has order 1344
and is strongly generated by the following 9 elements:
(
1 0 0 0 
0 1 0 0 
0 0 1 0 
1 0 1 1 
, 
1 0 0 0 
0 1 0 0 
0 0 1 0 
1 1 0 1 
, 
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 
0 1 0 0 
1 0 1 1 
0 0 0 1 
, 
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 0 1 1 
0 0 1 0 
1 1 0 1 
1 0 0 0 
, 
0 1 1 1 
0 0 0 1 
0 0 1 0 
1 0 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 7)(6, 8), 
(4, 6)(7, 8), 
(3, 5)(4, 6), 
(3, 4)(5, 6), 
(3, 7)(5, 8), 
(2, 7)(3, 5, 6, 4), 
(2, 5, 3)(4, 6, 7), 
(1, 4, 6, 3, 2, 5, 7), 
(1, 8)(2, 5, 7, 4)
orbits: { 1, 7, 8, 4, 3, 2, 6, 5 }