the 1 isometry classes of irreducible [5,2,4]_5 codes are:

code no       1:
================
1 1 1 4 0
3 2 1 0 4
the automorphism group has order 20
and is strongly generated by the following 2 elements:
(
1 0 0 
4 1 3 
0 4 0 
, 
0 0 2 
2 0 0 
3 3 3 
)
acting on the columns of the generator matrix as follows (in order):
(2, 3, 4, 5), 
(1, 2, 4, 3)
orbits: { 1, 3, 2, 4, 5 }