the 2 isometry classes of irreducible [8,2,4]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 0
1 1 1 0 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 1 1 1 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 1 1 1 1 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
1 1 1 1 1 1 
, 
1 0 0 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 0 0 0 0 1 
1 1 1 1 1 1 
0 0 0 0 1 0 
, 
0 0 1 0 0 0 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 1 1 1 
0 0 0 0 1 0 
0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(5, 7), 
(4, 7, 6, 5), 
(2, 3)(4, 7, 5, 6), 
(1, 2, 3)(4, 6, 7)
orbits: { 1, 3, 2 }, { 4, 5, 6, 7 }, { 8 }

code no       2:
================
1 1 1 0 0 0 1 0
1 1 0 1 1 1 0 1
the automorphism group has order 192
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 0 1 1 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
0 0 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 0 0 1 
0 0 0 1 0 0 
0 0 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 1 1 
0 0 0 0 0 1 
0 0 0 1 0 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
0 0 0 1 0 0 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 8), 
(5, 6), 
(4, 5, 6), 
(4, 6, 5, 8), 
(3, 7)(4, 5), 
(1, 2)(3, 7)(4, 6, 5), 
(1, 7)(2, 3)(4, 6, 5)
orbits: { 1, 2, 7, 3 }, { 4, 6, 8, 5 }