the 2 isometry classes of irreducible [10,3,5]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 0 0
1 1 1 1 0 0 0 0 1 0
1 1 0 0 1 1 0 0 0 1
the automorphism group has order 128
and is strongly generated by the following 6 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 1 1 1 1 1 1 
, 
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 0 1 0 
0 0 0 0 1 0 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 1 0 0 0 
0 0 1 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 
, 
1 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 1 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
1 1 1 1 1 1 1 
, 
1 1 1 1 1 1 1 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
0 0 0 0 1 0 0 
0 0 0 1 0 0 0 
0 0 1 0 0 0 0 
1 0 0 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 
1 0 0 0 0 0 0 
0 0 0 0 0 0 1 
1 1 1 1 1 1 1 
0 0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(7, 8), 
(5, 6), 
(3, 4)(5, 6), 
(3, 5)(4, 6)(7, 8)(9, 10), 
(1, 7, 2, 8)(3, 6)(4, 5), 
(1, 4)(2, 3)(5, 7)(6, 8)
orbits: { 1, 8, 4, 7, 2, 6, 3, 5 }, { 9, 10 }

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