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

code no       1:
================
1 1 1 1 1 1
the automorphism group has order 1440
and is strongly generated by the following 8 elements:
(
2 0 0 0 0 
0 2 0 0 0 
0 0 2 0 0 
0 0 0 2 0 
0 0 0 0 2 
, 1
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 1 1 1 
, 1
, 
2 0 0 0 0 
0 2 0 0 0 
0 0 2 0 0 
0 0 0 0 2 
0 0 0 2 0 
, 0
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 1 1 1 
0 0 0 0 1 
, 1
, 
2 0 0 0 0 
0 2 0 0 0 
0 0 0 2 0 
0 0 2 0 0 
0 0 0 0 2 
, 0
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 1
, 
0 0 2 0 0 
0 0 0 2 0 
0 0 0 0 2 
2 0 0 0 0 
0 2 0 0 0 
, 1
, 
3 3 3 3 3 
0 0 0 3 0 
0 3 0 0 0 
0 0 0 0 3 
3 0 0 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
id, 
(5, 6), 
(4, 5), 
(4, 6), 
(3, 4), 
(2, 3), 
(1, 4, 2, 5, 3), 
(1, 5, 4, 2, 3, 6)
orbits: { 1, 3, 6, 4, 2, 5 }