the 1 isometry classes of irreducible [6,3,4]_4 codes are:

code no       1:
================
1 1 1 1 0 0
3 2 1 0 1 0
2 3 1 0 0 1
the automorphism group has order 720
and is strongly generated by the following 9 elements:
(
3 0 0 
0 3 0 
0 0 3 
, 1
, 
2 0 0 
0 3 0 
0 0 1 
, 1
, 
2 0 0 
0 1 0 
2 1 3 
, 0
, 
3 0 0 
0 2 0 
3 2 1 
, 1
, 
3 0 0 
0 0 2 
2 1 3 
, 0
, 
0 0 3 
3 0 0 
0 3 0 
, 0
, 
3 3 3 
0 0 3 
0 3 0 
, 0
, 
1 3 2 
0 1 0 
3 0 0 
, 0
, 
1 2 3 
0 0 1 
2 2 2 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(5, 6), 
(4, 5), 
(3, 4, 5), 
(3, 4, 5, 6), 
(2, 5, 3), 
(1, 2, 3), 
(1, 4)(2, 3), 
(1, 3, 5), 
(1, 4, 3, 2, 6)
orbits: { 1, 3, 4, 5, 6, 2 }