the 2 isometry classes of irreducible [8,3,6]_8 codes are:

code no       1:
================
1 1 1 1 1 1 0 0
5 4 3 2 1 0 1 0
7 2 5 3 1 0 0 1
the automorphism group has order 42
and is strongly generated by the following 4 elements:
(
7 0 0 0 0 
6 6 6 6 6 
0 0 0 0 6 
0 0 0 3 0 
3 1 2 4 5 
, 1
, 
2 0 0 0 0 
1 4 5 7 3 
0 7 0 0 0 
0 0 0 4 0 
3 3 3 3 3 
, 1
, 
3 5 4 2 6 
3 0 0 0 0 
0 0 0 0 6 
0 0 0 2 0 
0 5 0 0 0 
, 2
, 
7 3 4 6 5 
0 1 0 0 0 
6 0 0 0 0 
0 0 0 1 0 
6 6 6 6 6 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(2, 7, 6)(3, 8, 5), 
(2, 3, 6, 5, 7, 8), 
(1, 2, 5, 3, 6, 7), 
(1, 3, 7, 6, 5, 8)
orbits: { 1, 7, 8, 2, 5, 6, 3 }, { 4 }

code no       2:
================
1 1 1 1 1 1 0 0
5 4 3 2 1 0 1 0
4 3 6 5 1 0 0 1
the automorphism group has order 168
and is strongly generated by the following 6 elements:
(
5 0 0 0 0 
0 7 0 0 0 
3 3 3 3 3 
6 4 1 3 2 
0 0 2 0 0 
, 1
, 
3 0 0 0 0 
6 6 6 6 6 
0 0 0 0 5 
0 0 1 0 0 
0 0 0 2 0 
, 1
, 
6 0 0 0 0 
0 0 0 2 0 
0 3 0 0 0 
0 0 1 0 0 
6 3 1 2 4 
, 2
, 
0 0 0 0 7 
0 5 0 0 0 
0 0 0 3 0 
2 2 2 2 2 
2 7 4 1 5 
, 1
, 
5 5 5 5 5 
0 0 7 0 0 
0 0 0 2 0 
3 0 0 0 0 
0 6 0 0 0 
, 0
, 
7 5 3 6 1 
4 0 0 0 0 
0 0 0 0 7 
3 5 4 2 6 
0 0 7 0 0 
, 2
)
acting on the columns of the generator matrix as follows (in order):
(3, 5, 6)(4, 8, 7), 
(2, 7, 6)(3, 4, 5), 
(2, 3, 4)(5, 6, 8), 
(1, 7, 5)(3, 6, 4), 
(1, 4, 3, 2, 5, 7, 6), 
(1, 2, 7, 4, 6, 8)(3, 5)
orbits: { 1, 5, 6, 8, 3, 4, 7, 2 }