the 1 isometry classes of irreducible [10,6,4]_3 codes are:

code no       1:
================
1 1 1 1 2 0 0 0 0 0
2 1 1 0 0 2 0 0 0 0
1 2 0 1 0 0 2 0 0 0
2 2 1 1 0 0 0 2 0 0
2 0 2 1 0 0 0 0 2 0
0 1 2 1 0 0 0 0 0 2
the automorphism group has order 1440
and is strongly generated by the following 7 elements:
(
2 0 0 0 
0 2 0 0 
0 0 2 0 
1 2 0 1 
, 
1 0 0 0 
0 1 0 0 
0 0 0 2 
0 0 2 0 
, 
1 0 0 0 
0 2 0 0 
2 2 2 2 
0 2 1 2 
, 
1 0 0 0 
1 2 2 0 
0 0 1 0 
2 2 1 1 
, 
1 0 0 0 
0 0 2 0 
2 1 0 2 
2 0 2 1 
, 
0 0 1 0 
2 1 0 2 
0 1 0 0 
1 1 2 2 
, 
0 2 1 2 
1 0 0 0 
0 0 0 1 
0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 7)(5, 10)(8, 9), 
(3, 4)(5, 8)(6, 7), 
(3, 9, 7, 8, 6, 10, 4, 5), 
(2, 6)(4, 8)(7, 9), 
(2, 8, 6, 5, 9, 4, 7, 3), 
(1, 7, 2, 3)(4, 5, 6, 8), 
(1, 2, 9, 10)(3, 4)(5, 7, 8, 6)
orbits: { 1, 3, 10, 4, 5, 7, 2, 6, 9, 8 }