the 3 isometry classes of irreducible [8,2,6]_5 codes are:

code no       1:
================
1 1 1 1 1 1 4 0
3 2 2 1 1 0 0 4
the automorphism group has order 16
and is strongly generated by the following 4 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 
4 4 4 4 4 4 
, 
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 0 
0 0 0 0 0 1 
, 
2 0 0 0 0 0 
0 0 2 0 0 0 
0 2 0 0 0 0 
0 0 0 0 2 0 
0 0 0 2 0 0 
3 3 3 3 3 3 
, 
4 1 1 3 3 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
1 1 1 1 1 1 
0 0 0 0 0 4 
0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(4, 5), 
(2, 3)(4, 5)(6, 7), 
(1, 8)(4, 6, 5, 7)
orbits: { 1, 8 }, { 2, 3 }, { 4, 5, 7, 6 }

code no       2:
================
1 1 1 1 1 1 4 0
4 3 2 1 1 0 0 4
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
0 0 0 3 0 0 
0 0 0 0 3 0 
2 2 2 2 2 2 
, 
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
0 0 0 0 3 0 
0 0 0 3 0 0 
0 0 0 0 0 3 
, 
3 0 0 0 0 0 
3 1 4 2 2 0 
0 0 2 0 0 0 
0 0 0 0 0 1 
4 4 4 4 4 4 
0 0 0 0 4 0 
, 
0 0 2 0 0 0 
0 2 0 0 0 0 
2 0 0 0 0 0 
0 0 0 0 0 2 
3 3 3 3 3 3 
0 0 0 2 0 0 
, 
2 4 1 3 3 0 
4 0 0 0 0 0 
0 2 0 0 0 0 
0 0 0 0 3 0 
0 0 0 3 0 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(4, 5), 
(2, 8)(4, 7, 5, 6), 
(1, 3)(4, 6)(5, 7), 
(1, 2, 3, 8)(4, 5)
orbits: { 1, 3, 8, 2 }, { 4, 5, 6, 7 }

code no       3:
================
1 1 1 1 1 0 4 0
2 2 1 1 0 1 0 4
the automorphism group has order 128
and is strongly generated by the following 6 elements:
(
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
0 0 0 3 0 0 
0 0 0 0 3 0 
4 4 2 2 0 2 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
4 4 4 4 4 0 
0 0 0 0 0 1 
, 
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 0 3 0 0 
0 0 3 0 0 0 
2 2 2 2 2 0 
0 0 0 0 0 3 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
3 3 4 4 0 4 
0 0 0 0 0 1 
0 0 0 0 4 0 
0 0 0 1 0 0 
, 
2 2 2 2 2 0 
0 0 0 0 3 0 
0 0 3 0 0 0 
0 0 0 3 0 0 
3 0 0 0 0 0 
0 0 0 0 0 2 
, 
2 2 1 1 0 1 
0 0 0 0 0 4 
3 3 3 3 3 0 
0 0 0 0 2 0 
0 0 1 0 0 0 
3 0 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 8), 
(5, 7), 
(3, 4)(5, 7), 
(3, 8)(4, 6), 
(1, 5, 2, 7), 
(1, 6, 2, 8)(3, 5, 4, 7)
orbits: { 1, 7, 8, 5, 2, 4, 6, 3 }