the 1 isometry classes of irreducible [4,1,4]_3 codes are:

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