the 4 isometry classes of irreducible [8,2,5]_4 codes are:

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

code no       2:
================
1 1 1 1 1 1 1 0
2 2 1 1 0 0 0 1
the automorphism group has order 48
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 
3 3 3 3 3 3 
, 0
, 
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 0 3 
0 0 0 0 3 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 0 
1 1 1 1 1 1 
0 0 0 0 1 0 
, 0
, 
2 0 0 0 0 0 
0 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
, 
0 0 0 2 0 0 
0 0 2 0 0 0 
2 0 0 0 0 0 
0 2 0 0 0 0 
2 2 2 2 2 2 
0 0 0 0 0 2 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(5, 6), 
(5, 6, 7), 
(3, 4)(5, 6), 
(1, 3, 2, 4)(5, 7)
orbits: { 1, 4, 3, 2 }, { 5, 6, 7 }, { 8 }

code no       3:
================
1 1 1 1 1 1 1 0
3 2 1 1 0 0 0 1
the automorphism group has order 72
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 
3 3 3 3 3 3 
, 0
, 
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
0 0 0 3 0 0 
3 3 3 3 3 3 
0 0 0 0 3 0 
, 0
, 
2 0 0 0 0 0 
0 2 0 0 0 0 
0 0 0 2 0 0 
0 0 2 0 0 0 
0 0 0 0 2 0 
0 0 0 0 0 2 
, 0
, 
2 0 0 0 0 0 
3 1 2 2 0 0 
0 0 0 3 0 0 
0 0 3 0 0 0 
0 0 0 0 0 1 
0 0 0 0 1 0 
, 1
, 
0 3 0 0 0 0 
3 0 0 0 0 0 
0 0 0 3 0 0 
0 0 3 0 0 0 
0 0 0 0 3 0 
0 0 0 0 0 3 
, 1
, 
3 2 1 1 0 0 
1 0 0 0 0 0 
0 0 3 0 0 0 
0 0 0 3 0 0 
2 2 2 2 2 2 
0 0 0 0 0 2 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(5, 6, 7), 
(3, 4), 
(2, 8)(3, 4)(5, 6), 
(1, 2)(3, 4), 
(1, 2, 8)(5, 7)
orbits: { 1, 2, 8 }, { 3, 4 }, { 5, 7, 6 }

code no       4:
================
1 1 1 1 0 0 1 0
1 1 0 0 1 1 0 1
the automorphism group has order 288
and is strongly generated by the following 8 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 
0 0 0 0 0 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 1 0 
1 1 0 0 1 1 
, 0
, 
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 0 3 
0 0 0 0 3 0 
, 1
, 
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
0 0 0 3 0 0 
3 3 0 0 3 3 
0 0 0 0 0 3 
, 0
, 
3 0 0 0 0 0 
0 3 0 0 0 0 
0 0 3 0 0 0 
3 3 3 3 0 0 
0 0 0 0 0 3 
0 0 0 0 3 0 
, 0
, 
2 0 0 0 0 0 
0 2 0 0 0 0 
2 2 2 2 0 0 
0 0 2 0 0 0 
0 0 0 0 2 0 
0 0 0 0 0 2 
, 0
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 0 1 1 
0 0 0 0 0 1 
0 0 0 1 0 0 
0 0 1 0 0 0 
, 1
, 
0 2 0 0 0 0 
2 0 0 0 0 0 
0 0 2 0 0 0 
2 2 2 2 0 0 
0 0 0 0 0 2 
0 0 0 0 2 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(6, 8), 
(5, 6), 
(5, 8), 
(4, 7)(5, 6), 
(3, 4, 7), 
(3, 6, 4, 5, 7, 8), 
(1, 2)(4, 7)(5, 6)
orbits: { 1, 2 }, { 3, 7, 8, 4, 5, 6 }