the 7 isometry classes of irreducible [10,3,7]_5 codes are:

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

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

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

code no       4:
================
1 1 1 1 1 1 1 4 0 0
3 3 2 2 1 1 0 0 4 0
3 2 3 1 2 0 1 0 0 4
the automorphism group has order 24
and is strongly generated by the following 4 elements:
(
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 2 0 0 
0 0 0 2 0 0 0 
0 0 0 0 0 0 2 
0 0 0 0 0 2 0 
, 
4 0 0 0 0 0 0 
3 3 2 2 1 1 0 
0 0 0 0 0 0 3 
0 0 0 0 4 0 0 
4 4 4 4 4 4 4 
0 2 0 0 0 0 0 
4 1 4 3 1 0 3 
, 
3 3 3 3 3 3 3 
0 0 0 0 0 0 2 
0 0 0 0 0 2 0 
0 0 0 0 2 0 0 
0 0 0 2 0 0 0 
0 0 2 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 
3 3 3 3 3 3 3 
2 0 0 0 0 0 0 
0 2 0 0 0 0 0 
0 0 0 0 0 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(4, 5)(6, 7)(9, 10), 
(2, 6, 9)(3, 10, 7)(4, 8, 5), 
(1, 8)(2, 7)(3, 6)(4, 5), 
(1, 5, 8, 4)(2, 6, 7, 3)
orbits: { 1, 8, 4, 5 }, { 2, 3, 9, 7, 6, 10 }

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

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

code no       7:
================
1 1 1 1 1 1 1 4 0 0
4 3 2 2 1 1 0 0 4 0
3 3 1 0 4 2 1 0 0 4
the automorphism group has order 120
and is strongly generated by the following 5 elements:
(
2 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 2 0 
0 0 0 0 2 0 0 
3 3 3 3 3 3 3 
, 
1 0 0 0 0 0 0 
1 2 3 3 4 4 0 
0 0 0 4 0 0 0 
0 0 4 0 0 0 0 
3 3 3 3 3 3 3 
0 0 0 0 0 0 2 
0 0 0 0 0 3 0 
, 
1 0 0 0 0 0 0 
2 2 2 2 2 2 2 
3 3 1 0 4 2 1 
0 0 0 1 0 0 0 
0 0 0 0 0 0 2 
4 3 2 2 1 1 0 
0 0 0 0 3 0 0 
, 
2 4 1 1 3 3 0 
2 0 0 0 0 0 0 
0 0 0 0 0 1 0 
0 0 0 0 1 0 0 
1 1 1 1 1 1 1 
0 0 0 0 0 0 4 
0 0 0 3 0 0 0 
, 
1 1 2 0 3 4 2 
0 0 0 0 1 0 0 
0 3 0 0 0 0 0 
3 0 0 0 0 0 0 
0 0 2 0 0 0 0 
0 0 0 0 0 0 2 
0 0 0 4 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(5, 6)(7, 8), 
(2, 9)(3, 4)(5, 8)(6, 7), 
(2, 8)(3, 10)(5, 7)(6, 9), 
(1, 2, 9)(3, 8, 5, 4, 7, 6), 
(1, 4, 7, 6, 9, 10)(2, 3, 5)
orbits: { 1, 9, 10, 2, 6, 3, 8, 5, 7, 4 }