the 2 isometry classes of irreducible [10,2,4]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 0
1 1 1 0 0 0 0 0 0 1
the automorphism group has order 4320
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 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 
1 1 1 1 1 1 1 1 
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 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 
1 1 1 1 1 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 
0 0 0 0 0 0 1 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 
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 0 0 0 0 1 
0 0 0 0 0 1 0 0 
0 0 0 0 1 0 0 0 
1 1 1 1 1 1 1 1 
0 0 0 0 0 0 1 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 
1 1 1 1 1 1 1 1 
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 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 0 1 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 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9), 
(7, 9), 
(6, 7), 
(6, 8, 9), 
(5, 6, 9, 8, 7), 
(4, 9, 7, 8)(5, 6), 
(2, 3)(4, 8, 9)(5, 6), 
(1, 3)(4, 6, 5, 7)
orbits: { 1, 3, 2 }, { 4, 8, 9, 7, 6, 5 }, { 10 }

code no       2:
================
1 1 1 0 0 0 0 0 1 0
1 1 0 1 1 1 1 1 0 1
the automorphism group has order 5760
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 0 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 
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 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 0 1 1 1 1 1 
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 
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 
, 
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 0 0 0 1 
0 0 0 0 1 0 0 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 0 1 1 1 1 1 
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 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 1 0 0 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 
1 1 0 1 1 1 1 1 
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 
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
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 0 0 1 
0 0 0 0 0 0 1 0 
0 0 0 0 0 1 0 0 
, 
1 1 1 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 0 0 1 
0 0 0 1 0 0 0 0 
0 0 0 0 0 0 1 0 
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, 7, 8), 
(6, 8, 7, 10), 
(5, 6), 
(5, 7)(6, 8), 
(5, 6, 7, 8, 10), 
(4, 7, 6), 
(4, 5, 6, 8, 7, 10), 
(3, 9)(4, 5)(6, 8), 
(1, 9)(2, 3)(4, 6, 8, 5)
orbits: { 1, 9, 3, 2 }, { 4, 6, 10, 5, 8, 7 }