the 1 isometry classes of irreducible [5,1,5]_8 codes are:

code no       1:
================
1 1 1 1 1
the automorphism group has order 360
and is strongly generated by the following 9 elements:
(
7 0 0 0 
0 7 0 0 
0 0 7 0 
0 0 0 7 
, 1
, 
6 0 0 0 
0 6 0 0 
0 0 6 0 
6 6 6 6 
, 2
, 
2 0 0 0 
0 2 0 0 
0 0 0 2 
0 0 2 0 
, 2
, 
1 0 0 0 
0 1 0 0 
1 1 1 1 
0 0 0 1 
, 2
, 
6 0 0 0 
0 0 0 6 
0 0 6 0 
0 6 0 0 
, 2
, 
5 0 0 0 
5 5 5 5 
0 0 0 5 
0 5 0 0 
, 1
, 
0 0 4 0 
0 4 0 0 
4 0 0 0 
0 0 0 4 
, 1
, 
0 2 0 0 
2 0 0 0 
0 0 2 0 
0 0 0 2 
, 0
, 
6 6 6 6 
0 6 0 0 
0 0 0 6 
0 0 6 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(4, 5), 
(3, 4), 
(3, 5), 
(2, 4), 
(2, 4, 3, 5), 
(1, 3), 
(1, 2), 
(1, 5)(3, 4)
orbits: { 1, 3, 2, 5, 4 }