the 2 isometry classes of irreducible [10,4,6]_4 codes are:

code no       1:
================
1 1 1 1 1 1 1 0 0 0
3 2 2 1 1 0 0 1 0 0
3 3 1 2 0 1 0 0 1 0
2 3 2 3 1 1 0 0 0 1
the automorphism group has order 20
and is strongly generated by the following 3 elements:
(
2 0 0 0 0 0 
0 0 0 1 0 0 
0 0 2 0 0 0 
0 1 0 0 0 0 
0 0 0 0 0 3 
0 0 0 0 3 0 
, 1
, 
2 2 1 3 0 1 
0 0 0 0 0 1 
0 0 0 2 0 0 
0 0 2 0 0 0 
0 0 0 0 1 0 
0 1 0 0 0 0 
, 1
, 
0 0 0 0 0 1 
3 1 3 1 2 2 
1 1 1 1 1 1 
1 1 2 3 0 2 
2 1 1 3 3 0 
1 0 0 0 0 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(2, 4)(5, 6)(7, 10)(8, 9), 
(1, 9)(2, 6)(3, 4)(7, 8), 
(1, 6)(2, 10)(3, 7)(4, 9)(5, 8)
orbits: { 1, 9, 6, 8, 4, 5, 2, 7, 3, 10 }

code no       2:
================
1 1 1 1 1 1 1 0 0 0
3 2 2 1 1 0 0 1 0 0
3 3 1 2 0 1 0 0 1 0
2 3 0 3 2 1 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 
0 2 0 0 0 0 
3 3 3 3 3 3 
0 0 0 2 0 0 
0 0 0 0 1 0 
2 1 0 1 2 3 
, 1
, 
3 0 0 0 0 0 
0 0 0 0 2 0 
1 3 3 2 2 0 
0 0 0 3 0 0 
0 1 0 0 0 0 
0 0 0 0 0 3 
, 0
, 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 1 1 1 1 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 0 0 1 
, 1
, 
0 0 2 0 0 0 
0 2 0 0 0 0 
0 0 0 0 0 3 
3 1 1 2 2 0 
0 0 0 0 1 0 
3 3 3 3 3 3 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 7)(6, 10)(8, 9), 
(2, 5)(3, 8)(7, 9), 
(1, 4)(2, 5)(3, 7)(8, 9), 
(1, 9, 10, 8, 4, 7, 6, 3)
orbits: { 1, 4, 3, 8, 7, 6, 9, 10 }, { 2, 5 }