the 1 isometry classes of irreducible [4,1,4]_8 codes are:

code no       1:
================
1 1 1 1
the automorphism group has order 72
and is strongly generated by the following 5 elements:
(
6 0 0 
0 6 0 
0 0 6 
, 2
, 
6 0 0 
0 6 0 
6 6 6 
, 1
, 
5 0 0 
0 0 5 
0 5 0 
, 2
, 
0 7 0 
7 0 0 
0 0 7 
, 1
, 
4 4 4 
0 0 4 
4 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(3, 4), 
(2, 3), 
(1, 2), 
(1, 3, 2, 4)
orbits: { 1, 2, 4, 3 }