the 2 isometry classes of irreducible [10,2,7]_3 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 2 0
2 2 2 1 1 1 0 0 0 2
the automorphism group has order 1296
and is strongly generated by the following 8 elements:
(
2 0 0 0 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 0 0 0 2 0 0 0 
0 0 0 0 0 2 0 0 
0 0 0 0 0 0 2 0 
1 1 1 1 1 1 1 1 
, 
1 0 0 0 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 0 0 0 1 0 0 0 
0 0 0 0 0 1 0 0 
2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 1 
, 
1 0 0 0 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 0 0 0 0 1 0 0 
0 0 0 0 1 0 0 0 
2 2 2 2 2 2 2 2 
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 0 2 0 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 0 0 2 0 
0 0 0 0 0 0 0 2 
, 
2 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 
0 0 0 0 0 0 2 0 
1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 2 
0 0 0 2 0 0 0 0 
0 0 0 0 0 2 0 0 
, 
1 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 1 0 0 0 0 
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 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 1 
2 2 2 2 2 2 2 2 
, 
2 2 2 2 2 2 2 2 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 
0 1 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9), 
(7, 9), 
(5, 6)(7, 9), 
(4, 6, 5), 
(4, 7)(5, 9)(6, 8), 
(2, 3)(4, 5), 
(1, 2, 3)(4, 5)(7, 9, 8), 
(1, 5, 8, 3, 6, 7, 2, 4, 9)
orbits: { 1, 3, 9, 2, 8, 7, 5, 4, 6 }, { 10 }

code no       2:
================
1 1 1 1 1 1 0 0 2 0
2 2 1 1 0 0 1 1 0 2
the automorphism group has order 576
and is strongly generated by the following 8 elements:
(
1 0 0 0 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 0 0 0 1 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 0 0 1 0 
1 1 2 2 0 0 2 2 
, 
2 0 0 0 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 0 0 0 2 0 0 0 
0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 2 
0 0 0 0 0 0 2 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 
0 0 0 2 0 0 0 0 
0 0 0 0 2 0 0 0 
1 1 1 1 1 1 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 
, 
2 0 0 0 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 0 0 0 0 2 0 0 
1 1 1 1 1 1 0 0 
0 0 0 0 0 0 0 2 
0 0 0 0 0 0 2 0 
, 
2 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 1 
1 1 2 2 0 0 2 2 
2 2 2 2 2 2 0 0 
0 0 0 0 1 0 0 0 
, 
2 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 
0 0 2 0 0 0 0 0 
0 0 0 0 0 2 0 0 
0 0 0 0 2 0 0 0 
0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 2 
, 
0 1 0 0 0 0 0 0 
1 0 0 0 0 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 
2 2 2 2 2 2 0 0 
0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 
, 
0 0 0 1 0 0 0 0 
0 0 1 0 0 0 0 0 
0 1 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 2 
0 0 0 0 0 0 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(8, 10), 
(7, 8), 
(6, 9), 
(5, 9, 6)(7, 8), 
(5, 8)(6, 10)(7, 9), 
(3, 4)(5, 6), 
(1, 2)(6, 9)(7, 8), 
(1, 4)(2, 3)(5, 6)(7, 8)
orbits: { 1, 2, 4, 3 }, { 5, 6, 8, 9, 10, 7 }