the 7 isometry classes of irreducible [8,2,5]_5 codes are:

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

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

code no       3:
================
1 1 1 1 1 1 4 0
2 2 1 1 0 0 0 4
the automorphism group has order 24
and is strongly generated by the following 4 elements:
(
2 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
0 0 0 2 0 0 
0 0 0 0 2 0 
3 3 3 3 3 3 
, 
2 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
0 0 0 2 0 0 
0 0 0 0 0 2 
0 0 0 0 2 0 
, 
4 0 0 0 0 0 
0 4 0 0 0 0 
0 0 0 4 0 0 
0 0 4 0 0 0 
1 1 1 1 1 1 
0 0 0 0 0 4 
, 
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 
2 2 2 2 2 2 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(5, 6), 
(3, 4)(5, 7), 
(1, 2)(3, 4)(6, 7)
orbits: { 1, 2 }, { 3, 4 }, { 5, 6, 7 }, { 8 }

code no       4:
================
1 1 1 1 1 1 4 0
3 2 1 1 0 0 0 4
the automorphism group has order 12
and is strongly generated by the following 3 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 
, 
2 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
0 0 0 2 0 0 
3 3 3 3 3 3 
0 0 0 0 2 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 0 
4 4 4 4 4 4 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(5, 6, 7), 
(3, 4)(6, 7)
orbits: { 1 }, { 2 }, { 3, 4 }, { 5, 7, 6 }, { 8 }

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

code no       6:
================
1 1 1 1 1 1 4 0
4 3 2 1 0 0 0 4
the automorphism group has order 120
and is strongly generated by the following 5 elements:
(
4 0 0 0 0 0 
0 4 0 0 0 0 
0 0 4 0 0 0 
0 0 0 4 0 0 
0 0 0 0 4 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 
0 0 0 0 0 1 
4 4 4 4 4 4 
, 
4 0 0 0 0 0 
0 0 1 0 0 0 
0 0 0 2 0 0 
4 3 2 1 0 0 
2 2 2 2 2 2 
0 0 0 0 3 0 
, 
0 0 3 0 0 0 
3 0 0 0 0 0 
0 0 0 3 0 0 
0 3 0 0 0 0 
0 0 0 0 0 3 
0 0 0 0 3 0 
, 
3 1 4 2 0 0 
0 0 3 0 0 0 
4 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 0 0 2 
0 0 0 0 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(5, 7, 6), 
(2, 8, 4, 3)(5, 6, 7), 
(1, 2, 4, 3)(5, 6), 
(1, 3, 2, 4, 8)(5, 6)
orbits: { 1, 3, 8, 4, 2 }, { 5, 6, 7 }

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