the 6 isometry classes of irreducible [10,3,6]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 2 0 0
2 2 1 1 1 0 0 0 2 0
2 1 2 1 0 1 0 0 0 2
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 2 0 
1 1 1 1 1 1 1 
, 
2 0 0 0 0 0 0 
2 2 1 1 1 0 0 
0 0 0 0 1 0 0 
0 0 0 2 0 0 0 
1 2 1 2 0 2 0 
0 1 0 0 0 0 0 
1 1 1 1 1 1 1 
, 
2 0 0 0 0 0 0 
0 0 2 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 0 2 0 
0 0 0 0 2 0 0 
0 0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(7, 8), 
(2, 6, 9)(3, 10, 5)(7, 8), 
(2, 3)(5, 6)(9, 10)
orbits: { 1 }, { 2, 9, 3, 6, 10, 5 }, { 4 }, { 7, 8 }

code no       2:
================
1 1 1 1 1 1 1 2 0 0
2 2 1 1 1 0 0 0 2 0
2 0 2 2 1 1 0 0 0 2
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 2 0 
1 1 1 1 1 1 1 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 0 1 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 1 0 
0 0 0 0 0 0 1 
, 
2 0 0 0 0 0 0 
1 0 1 1 2 2 0 
0 0 0 0 0 0 1 
2 2 2 2 2 2 2 
1 1 2 2 2 0 0 
0 0 0 0 0 2 0 
0 0 0 1 0 0 0 
, 
0 2 0 0 0 0 0 
2 0 0 0 0 0 0 
0 0 0 0 0 0 2 
1 1 1 1 1 1 1 
0 0 0 0 0 2 0 
0 0 0 0 2 0 0 
0 0 0 2 0 0 0 
, 
0 0 0 0 2 0 0 
2 2 1 1 1 0 0 
2 2 2 2 2 2 2 
0 0 0 0 0 0 1 
2 0 2 2 1 1 0 
0 2 0 0 0 0 0 
0 0 0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(7, 8), 
(3, 4), 
(2, 10)(3, 8, 4, 7)(5, 9), 
(1, 2)(3, 8, 4, 7)(5, 6), 
(1, 9, 2, 6, 10, 5)(3, 8)(4, 7)
orbits: { 1, 2, 5, 10, 9, 6 }, { 3, 4, 7, 8 }

code no       3:
================
1 1 1 1 1 1 1 2 0 0
2 2 1 1 1 0 0 0 2 0
1 0 2 1 0 2 1 0 0 2
the automorphism group has order 24
and is strongly generated by the following 4 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 0 0 2 0 
0 0 0 0 0 0 2 
1 1 1 1 1 1 1 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
, 
2 0 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 0 2 0 
0 0 0 0 0 0 1 
2 0 1 2 0 1 2 
0 1 0 0 0 0 0 
2 2 1 1 1 0 0 
, 
0 1 0 0 0 0 0 
1 0 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 1 0 0 
0 0 0 1 0 0 0 
0 0 0 0 0 1 0 
2 2 2 2 2 2 2 
, 
0 0 0 0 0 1 0 
2 0 0 0 0 0 0 
0 0 2 0 0 0 0 
2 0 1 2 0 1 2 
0 0 0 1 0 0 0 
0 1 0 0 0 0 0 
1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 6)(4, 7)(5, 8), 
(2, 6, 3)(4, 9, 7)(5, 8, 10), 
(1, 2)(4, 5)(7, 8), 
(1, 2, 6)(4, 5, 10)(7, 9, 8)
orbits: { 1, 2, 6, 3 }, { 4, 7, 5, 10, 9, 8 }

code no       4:
================
1 1 1 1 1 0 0 2 0 0
2 2 1 1 0 1 0 0 2 0
2 1 2 1 0 0 1 0 0 2
the automorphism group has order 192
and is strongly generated by the following 7 elements:
(
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 0 0 0 2 0 
2 1 2 1 0 0 1 
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
2 2 1 1 0 1 0 
0 0 0 0 0 0 2 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
2 2 2 2 2 0 0 
1 1 2 2 0 2 0 
0 0 0 0 0 0 1 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 0 2 0 0 0 
0 0 2 0 0 0 0 
2 2 1 1 0 1 0 
1 1 1 1 1 0 0 
0 0 0 0 0 0 1 
, 
2 0 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 1 0 0 0 
0 1 0 0 0 0 0 
1 2 1 2 0 0 2 
2 2 2 2 2 0 0 
2 2 1 1 0 1 0 
, 
0 1 0 0 0 0 0 
1 0 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 2 0 0 0 
2 2 1 1 0 1 0 
0 0 0 0 2 0 0 
0 0 0 0 0 0 2 
, 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 2 0 0 0 0 0 
2 0 0 0 0 0 0 
1 1 2 2 0 2 0 
0 0 0 0 2 0 0 
0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(7, 10), 
(6, 9), 
(5, 8)(6, 9), 
(3, 4)(5, 9)(6, 8), 
(2, 4, 3)(5, 9, 7, 8, 6, 10), 
(1, 2)(5, 6, 8, 9), 
(1, 4, 2, 3)(5, 6, 8, 9)
orbits: { 1, 2, 3, 4 }, { 5, 8, 9, 10, 6, 7 }

code no       5:
================
1 1 1 1 1 0 0 2 0 0
2 2 1 1 0 1 0 0 2 0
2 1 2 0 1 1 1 0 0 2
the automorphism group has order 96
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 1 0 
1 2 1 0 2 2 2 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 0 0 2 0 0 
1 1 1 1 1 0 0 
0 0 0 0 0 1 0 
0 0 2 0 0 0 0 
0 0 0 0 0 0 1 
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 1 0 0 0 
0 0 1 0 0 0 0 
1 1 2 2 0 2 0 
2 2 2 2 2 0 0 
0 0 0 0 0 0 2 
, 
1 1 2 2 0 2 0 
0 0 0 0 0 1 0 
0 2 0 0 0 0 0 
2 0 0 0 0 0 0 
0 0 1 0 0 0 0 
2 2 2 2 2 0 0 
0 0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(7, 10), 
(3, 6, 5)(4, 9, 8), 
(3, 4)(5, 9)(6, 8), 
(1, 4, 8, 6, 2, 3, 5, 9)
orbits: { 1, 9, 4, 5, 8, 3, 6, 2 }, { 7, 10 }

code no       6:
================
1 1 1 1 1 0 0 2 0 0
1 1 1 0 0 1 1 0 2 0
2 1 0 2 1 2 1 0 0 2
the automorphism group has order 108
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 0 0 0 1 
2 2 2 0 0 2 2 
2 2 2 2 2 0 0 
0 0 0 1 0 0 0 
, 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 0 0 2 0 
0 0 0 0 0 0 2 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
, 
1 0 0 0 0 0 0 
0 0 1 0 0 0 0 
0 1 0 0 0 0 0 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
0 0 0 1 0 0 0 
2 2 2 2 2 0 0 
, 
1 1 1 1 1 0 0 
0 0 0 2 0 0 0 
0 0 0 0 2 0 0 
0 0 2 0 0 0 0 
2 0 0 0 0 0 0 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 7)(5, 9)(6, 8), 
(4, 6)(5, 7)(8, 9), 
(2, 3)(4, 6, 5, 9, 8, 7), 
(1, 5, 3, 4, 2, 8)(6, 7)
orbits: { 1, 8, 6, 9, 2, 4, 7, 5, 3 }, { 10 }