the 2 isometry classes of irreducible [10,2,6]_2 codes are:

code no       1:
================
1 1 1 1 1 0 0 0 1 0
1 1 0 0 0 1 1 1 0 1
the automorphism group has order 2304
and is strongly generated by the following 9 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 0 0 0 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 
0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 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 0 1 0 
0 0 0 0 0 0 0 1 
0 0 0 0 0 1 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 
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 
, 
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 1 1 1 1 0 0 0 
0 0 0 0 1 0 0 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 
, 
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 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 
, 
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 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 0 0 1 
0 0 0 0 0 1 0 0 
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
1 1 0 0 0 1 1 1 
0 0 0 0 0 0 0 1 
0 0 0 0 0 1 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 1 0 0 0 
1 1 1 1 1 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 0 1 0 
0 0 0 0 0 0 0 1 
0 0 0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(8, 10), 
(7, 8), 
(6, 8, 7), 
(5, 9), 
(4, 9)(6, 7, 8), 
(3, 4)(7, 8), 
(3, 4, 5)(6, 8, 7), 
(3, 10)(4, 6, 5, 7, 9, 8), 
(1, 2)(3, 4)(6, 8, 7)
orbits: { 1, 2 }, { 3, 4, 5, 10, 9, 8, 6, 7 }

code no       2:
================
1 1 1 1 1 0 0 0 1 0
1 1 1 0 0 1 1 1 0 1
the automorphism group has order 1728
and is strongly generated by the following 11 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 1 0 0 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 
0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 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 0 1 0 
0 0 0 0 0 1 0 0 
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 1 0 0 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 
, 
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 
1 1 1 0 0 1 1 1 
0 0 0 0 0 0 1 0 
0 0 0 0 0 1 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 
1 1 1 1 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 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 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 0 0 1 
0 0 0 0 0 1 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 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 0 0 1 
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 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 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 
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 1 0 0 0 
1 1 1 1 1 0 0 0 
0 0 0 1 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 0 1 0 
0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 10), 
(7, 8), 
(6, 7), 
(6, 7, 8), 
(6, 8, 10), 
(5, 9)(6, 7), 
(4, 5)(6, 8, 7), 
(2, 3)(6, 8, 7), 
(1, 3), 
(1, 2)(6, 7, 8), 
(1, 5)(2, 4, 3, 9)(6, 7)
orbits: { 1, 3, 2, 5, 4, 9 }, { 6, 7, 8, 10 }