the 19 isometry classes of irreducible [10,4,5]_3 codes are:

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

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

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

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

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

code no       6:
================
1 1 1 1 1 1 2 0 0 0
2 1 1 1 0 0 0 2 0 0
1 2 1 0 1 0 0 0 2 0
1 0 1 2 0 1 0 0 0 2
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
2 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
0 0 0 2 0 0 
1 2 1 0 1 0 
1 0 1 2 0 1 
, 
2 0 0 0 0 0 
0 0 0 2 0 0 
0 0 2 0 0 0 
0 2 0 0 0 0 
1 0 1 2 0 1 
1 2 1 0 1 0 
, 
1 2 2 2 0 0 
0 0 0 2 0 0 
0 0 2 0 0 0 
0 2 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
0 0 0 2 0 0 
1 2 2 2 0 0 
0 0 1 0 0 0 
2 0 0 0 0 0 
1 2 1 0 1 0 
0 0 0 0 0 1 
, 
2 0 2 1 0 2 
0 0 0 0 1 0 
1 1 1 1 1 1 
1 2 1 0 1 0 
0 2 0 0 0 0 
2 1 1 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 9)(6, 10), 
(2, 4)(5, 10)(6, 9), 
(1, 8)(2, 4), 
(1, 4)(2, 8)(5, 9), 
(1, 10)(2, 5)(3, 7)(4, 9)(6, 8)
orbits: { 1, 8, 4, 10, 2, 6, 9, 5 }, { 3, 7 }

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

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

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

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

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

code no      12:
================
1 1 1 1 1 1 2 0 0 0
2 1 1 1 0 0 0 2 0 0
2 2 1 0 1 0 0 0 2 0
0 1 1 2 0 1 0 0 0 2
the automorphism group has order 1
and is strongly generated by the following 0 elements:
(
)
acting on the columns of the generator matrix as follows (in order):
orbits: { 1 }, { 2 }, { 3 }, { 4 }, { 5 }, { 6 }, { 7 }, { 8 }, { 9 }, { 10 }

code no      13:
================
1 1 1 1 1 1 2 0 0 0
2 1 1 1 0 0 0 2 0 0
2 2 1 0 1 0 0 0 2 0
2 1 0 0 2 1 0 0 0 2
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
2 0 0 0 0 0 
0 0 0 0 2 0 
0 0 0 0 0 2 
1 1 1 1 1 1 
0 2 0 0 0 0 
0 0 2 0 0 0 
, 
2 1 1 1 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
0 0 0 0 2 0 
1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 5)(3, 6)(4, 7)(9, 10), 
(1, 8)(3, 4)(6, 7)
orbits: { 1, 8 }, { 2, 5 }, { 3, 6, 4, 7 }, { 9, 10 }

code no      14:
================
1 1 1 1 1 1 2 0 0 0
2 1 1 1 0 0 0 2 0 0
2 2 1 0 1 0 0 0 2 0
1 0 0 2 2 1 0 0 0 2
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
0 0 0 0 2 0 
0 1 0 0 0 0 
1 1 2 0 2 0 
2 1 1 1 0 0 
2 0 0 0 0 0 
0 0 0 0 0 2 
, 
2 1 1 1 0 0 
0 0 0 0 0 2 
1 1 1 1 1 1 
0 0 0 0 2 0 
0 0 0 1 0 0 
0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 5)(3, 9)(4, 8)(7, 10), 
(1, 8)(2, 6)(3, 7)(4, 5)(9, 10)
orbits: { 1, 5, 8, 4 }, { 2, 6 }, { 3, 9, 7, 10 }

code no      15:
================
1 1 1 1 1 1 2 0 0 0
2 2 1 1 0 0 0 2 0 0
2 1 2 0 1 0 0 0 2 0
0 2 2 1 1 0 0 0 0 2
the automorphism group has order 32
and is strongly generated by the following 3 elements:
(
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 2 0 
1 1 1 1 1 1 
, 
2 0 0 0 0 0 
0 0 2 0 0 0 
0 2 0 0 0 0 
0 0 0 0 2 0 
0 0 0 2 0 0 
0 0 0 0 0 2 
, 
2 2 1 1 0 0 
0 0 0 0 2 0 
1 0 0 0 0 0 
1 2 1 0 2 0 
0 0 2 0 0 0 
2 2 2 2 2 2 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(2, 3)(4, 5)(8, 9), 
(1, 3, 5, 2, 10, 9, 4, 8)(6, 7)
orbits: { 1, 8, 9, 4, 10, 5, 2, 3 }, { 6, 7 }

code no      16:
================
1 1 1 1 1 1 2 0 0 0
2 2 1 1 0 0 0 2 0 0
2 1 2 0 1 0 0 0 2 0
1 2 2 0 0 1 0 0 0 2
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 2 2 0 0 
1 2 1 0 2 0 
2 1 1 0 0 2 
, 
2 0 0 0 0 0 
0 0 2 0 0 0 
0 2 0 0 0 0 
0 0 0 0 2 0 
0 0 0 2 0 0 
0 0 0 0 0 2 
, 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 0 0 0 0 
2 1 1 0 0 2 
1 1 2 2 0 0 
1 2 1 0 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 8)(5, 9)(6, 10), 
(2, 3)(4, 5)(8, 9), 
(1, 3, 2)(4, 9, 6, 8, 5, 10)
orbits: { 1, 2, 3 }, { 4, 8, 5, 10, 9, 6 }, { 7 }

code no      17:
================
1 1 1 1 1 1 2 0 0 0
2 2 1 1 0 0 0 2 0 0
2 1 2 0 1 0 0 0 2 0
2 1 0 2 0 1 0 0 0 2
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
2 0 0 0 0 0 
0 2 0 0 0 0 
0 0 0 2 0 0 
0 0 2 0 0 0 
0 0 0 0 0 2 
0 0 0 0 2 0 
, 
2 0 0 0 0 0 
0 0 0 1 0 0 
2 2 1 1 0 0 
0 1 0 0 0 0 
1 2 1 0 2 0 
0 0 0 0 0 2 
, 
1 0 0 0 0 0 
0 0 2 0 0 0 
1 1 2 2 0 0 
0 2 0 0 0 0 
2 1 0 2 0 1 
0 0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(5, 6)(9, 10), 
(2, 4)(3, 8)(5, 9), 
(2, 4, 8, 3)(5, 6, 9, 10)
orbits: { 1 }, { 2, 4, 3, 8 }, { 5, 6, 9, 10 }, { 7 }

code no      18:
================
1 1 1 1 0 0 2 0 0 0
2 1 1 0 1 0 0 2 0 0
1 2 0 1 1 0 0 0 2 0
1 2 1 0 0 1 0 0 0 2
the automorphism group has order 16
and is strongly generated by the following 3 elements:
(
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 2 0 
1 2 1 0 0 1 
, 
2 0 0 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 2 2 0 2 0 
2 2 2 2 0 0 
0 0 0 0 0 2 
, 
2 2 2 2 0 0 
0 0 0 2 0 0 
0 2 0 0 0 0 
2 1 1 0 1 0 
2 0 0 0 0 0 
0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(6, 10), 
(2, 3)(4, 8)(5, 7), 
(1, 5, 9, 7)(2, 3, 8, 4)
orbits: { 1, 7, 5, 9 }, { 2, 3, 4, 8 }, { 6, 10 }

code no      19:
================
1 1 1 1 0 0 2 0 0 0
2 1 1 0 1 0 0 2 0 0
2 1 0 1 0 1 0 0 2 0
1 1 0 0 1 1 0 0 0 2
the automorphism group has order 72
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 2 0 0 0 0 
0 0 2 0 0 0 
0 0 0 0 2 0 
0 0 0 2 0 0 
0 0 0 0 0 2 
, 
1 0 0 0 0 0 
0 1 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 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
0 0 1 0 0 0 
0 0 0 1 0 0 
, 
2 0 0 0 0 0 
0 0 2 0 0 0 
1 1 1 1 0 0 
0 2 0 0 0 0 
0 0 0 0 0 1 
2 1 1 0 1 0 
, 
1 0 0 0 0 0 
1 1 0 0 1 1 
1 2 0 2 0 2 
0 0 0 0 2 0 
1 2 2 0 2 0 
0 0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(7, 8)(9, 10), 
(3, 4)(5, 6)(8, 9), 
(3, 5)(4, 6)(7, 10), 
(2, 4, 7, 3)(5, 9, 8, 6), 
(2, 9, 3, 10)(4, 7, 8, 5)
orbits: { 1 }, { 2, 3, 10, 4, 5, 7, 9, 6, 8 }