the 4 isometry classes of irreducible [10,2,7]_4 codes are:

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

code no       2:
================
1 1 1 1 1 1 1 1 1 0
3 2 2 1 1 1 0 0 0 1
the automorphism group has order 288
and is strongly generated by the following 6 elements:
(
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 3 0 0 0 0 
0 0 0 0 3 0 0 0 
0 0 0 0 0 3 0 0 
0 0 0 0 0 0 3 0 
3 3 3 3 3 3 3 3 
, 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 0 
0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 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 0 0 
2 2 2 2 2 2 2 2 
0 0 0 0 0 0 2 0 
, 0
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
3 3 3 3 3 3 3 3 
0 0 0 0 0 0 0 3 
0 0 0 0 0 0 3 0 
0 0 0 0 3 0 0 0 
0 0 0 3 0 0 0 0 
, 1
, 
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 0 0 2 0 0 
0 0 0 2 0 0 0 0 
2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 2 
, 0
, 
3 1 1 2 2 2 0 0 
0 0 2 0 0 0 0 0 
0 2 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 1 0 0 0 
3 3 3 3 3 3 3 3 
0 0 0 0 0 0 3 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(8, 9), 
(7, 8), 
(5, 6)(7, 8, 9), 
(4, 8, 5, 7, 6, 9), 
(2, 3)(4, 6, 5)(7, 9), 
(1, 10)(2, 3)(5, 6)(7, 8, 9)
orbits: { 1, 10 }, { 2, 3 }, { 4, 9, 5, 8, 6, 7 }

code no       3:
================
1 1 1 1 1 1 1 1 1 0
3 3 2 2 1 1 0 0 0 1
the automorphism group has order 288
and is strongly generated by the following 7 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 
2 2 2 2 2 2 2 2 
, 0
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 3 0 0 0 0 
0 0 0 0 3 0 0 0 
0 0 0 0 0 3 0 0 
0 0 0 0 0 0 0 3 
3 3 3 3 3 3 3 3 
, 0
, 
3 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 
0 0 0 3 0 0 0 0 
0 0 0 0 0 3 0 0 
0 0 0 0 3 0 0 0 
0 0 0 0 0 0 0 3 
3 3 3 3 3 3 3 3 
, 0
, 
1 0 0 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 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 
, 1
, 
2 0 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 0 2 0 0 
0 0 0 2 0 0 0 0 
0 0 2 0 0 0 0 0 
2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 2 
, 1
, 
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 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 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 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 1 
0 0 0 0 0 0 1 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(8, 9), 
(7, 9, 8), 
(5, 6)(7, 9, 8), 
(3, 6)(4, 5)(7, 8), 
(3, 6, 4, 5)(7, 9), 
(1, 3)(2, 4)(5, 6), 
(1, 2)(3, 6, 4, 5)(7, 8)
orbits: { 1, 3, 2, 6, 5, 4 }, { 7, 8, 9 }, { 10 }

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