the 19 isometry classes of irreducible [7,3,3]_4 codes are:

code no       1:
================
1 1 1 1 1 0 0
1 1 0 0 0 1 0
2 1 0 0 0 0 1
the automorphism group has order 36
and is strongly generated by the following 5 elements:
(
2 0 0 0 
0 2 0 0 
0 0 2 0 
2 2 2 2 
, 0
, 
2 0 0 0 
0 2 0 0 
2 2 2 2 
0 0 2 0 
, 0
, 
1 0 0 0 
2 3 0 0 
0 0 0 3 
0 0 3 0 
, 1
, 
0 2 0 0 
2 0 0 0 
0 0 2 0 
2 2 2 2 
, 1
, 
2 1 0 0 
3 0 0 0 
0 0 1 0 
0 0 0 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(4, 5), 
(3, 4, 5), 
(2, 7)(3, 4), 
(1, 2)(4, 5), 
(1, 2, 7)
orbits: { 1, 2, 7 }, { 3, 5, 4 }, { 6 }

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

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

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

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

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

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

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

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

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

code no      11:
================
1 1 1 1 1 0 0
1 1 0 0 0 1 0
3 3 2 1 0 0 1
the automorphism group has order 48
and is strongly generated by the following 6 elements:
(
2 0 0 0 
0 2 0 0 
0 0 3 0 
0 0 0 1 
, 1
, 
2 0 0 0 
0 2 0 0 
0 0 2 0 
2 2 2 2 
, 1
, 
3 0 0 0 
0 3 0 0 
0 0 2 0 
3 3 2 1 
, 0
, 
3 0 0 0 
0 3 0 0 
3 3 3 3 
0 0 3 0 
, 0
, 
3 0 0 0 
0 3 0 0 
2 2 3 1 
1 1 1 1 
, 1
, 
0 1 0 0 
1 0 0 0 
0 0 1 0 
1 1 1 1 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(5, 7), 
(4, 5), 
(4, 5, 7), 
(3, 4, 5), 
(3, 5, 4, 7), 
(1, 2)(4, 5)
orbits: { 1, 2 }, { 3, 5, 7, 4 }, { 6 }

code no      12:
================
1 1 1 1 1 0 0
2 1 0 0 0 1 0
3 1 0 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 8 elements:
(
1 0 0 0 
0 1 0 0 
0 0 1 0 
0 0 0 1 
, 1
, 
2 0 0 0 
0 2 0 0 
0 0 2 0 
2 2 2 2 
, 0
, 
2 0 0 0 
0 2 0 0 
2 2 2 2 
0 0 0 2 
, 0
, 
1 0 0 0 
0 1 0 0 
0 0 0 1 
0 0 1 0 
, 0
, 
1 0 0 0 
2 3 0 0 
3 3 3 3 
0 0 3 0 
, 1
, 
2 0 0 0 
1 3 0 0 
0 0 0 3 
0 0 3 0 
, 1
, 
0 1 0 0 
1 0 0 0 
0 0 0 1 
0 0 1 0 
, 1
, 
2 3 0 0 
0 1 0 0 
2 2 2 2 
0 0 0 2 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(4, 5), 
(3, 5), 
(3, 4), 
(2, 6)(3, 4, 5), 
(2, 7)(3, 4), 
(1, 2)(3, 4), 
(1, 6, 7)(3, 5)
orbits: { 1, 2, 7, 6 }, { 3, 5, 4 }

code no      13:
================
1 1 1 1 1 0 0
2 1 0 0 0 1 0
2 0 1 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
2 0 0 0 
0 2 0 0 
0 0 2 0 
2 2 2 2 
, 0
, 
3 0 0 0 
0 2 0 0 
1 0 2 0 
2 2 2 2 
, 1
, 
1 0 0 0 
2 3 0 0 
0 0 3 0 
0 0 0 3 
, 1
, 
2 0 0 0 
3 0 2 0 
3 2 0 0 
2 2 2 2 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(4, 5), 
(3, 7)(4, 5), 
(2, 6), 
(2, 7)(3, 6)(4, 5)
orbits: { 1 }, { 2, 6, 7, 3 }, { 4, 5 }

code no      14:
================
1 1 1 1 1 0 0
2 1 0 0 0 1 0
2 2 1 0 0 0 1
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
3 0 0 0 
0 3 0 0 
0 0 3 0 
3 3 3 3 
, 0
, 
2 0 0 0 
3 1 0 0 
2 2 3 0 
0 0 0 3 
, 1
, 
1 3 0 0 
2 0 0 0 
0 0 3 0 
0 0 0 3 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(4, 5), 
(2, 6)(3, 7), 
(1, 2, 6)
orbits: { 1, 6, 2 }, { 3, 7 }, { 4, 5 }

code no      15:
================
1 1 1 1 1 0 0
2 1 0 0 0 1 0
0 0 2 1 0 0 1
the automorphism group has order 36
and is strongly generated by the following 5 elements:
(
1 0 0 0 
0 1 0 0 
0 0 0 2 
0 0 1 3 
, 0
, 
2 0 0 0 
3 1 0 0 
0 0 0 1 
0 0 1 0 
, 1
, 
1 2 0 0 
0 3 0 0 
0 0 0 1 
0 0 1 0 
, 1
, 
0 1 0 0 
1 0 0 0 
0 0 0 1 
0 0 1 0 
, 1
, 
0 0 2 3 
0 0 0 1 
3 0 0 0 
1 2 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(3, 7, 4), 
(2, 6)(3, 4), 
(1, 6)(3, 4), 
(1, 2)(3, 4), 
(1, 3, 6, 4, 2, 7)
orbits: { 1, 6, 2, 7, 3, 4 }, { 5 }

code no      16:
================
1 1 1 1 1 0 0
2 1 0 0 0 1 0
3 3 2 1 0 0 1
the automorphism group has order 72
and is strongly generated by the following 6 elements:
(
3 0 0 0 
0 3 0 0 
0 0 2 0 
3 3 2 1 
, 0
, 
2 0 0 0 
0 2 0 0 
2 2 2 2 
0 0 2 0 
, 0
, 
3 0 0 0 
0 3 0 0 
3 3 2 1 
0 0 0 1 
, 0
, 
2 0 0 0 
3 1 0 0 
0 0 0 1 
0 0 1 0 
, 1
, 
3 1 0 0 
0 2 0 0 
0 0 3 0 
3 3 3 3 
, 1
, 
0 2 0 0 
2 0 0 0 
2 2 2 2 
0 0 0 2 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(4, 5, 7), 
(3, 4, 5), 
(3, 5, 7), 
(2, 6)(3, 4), 
(1, 6)(4, 5), 
(1, 2)(3, 5)
orbits: { 1, 6, 2 }, { 3, 5, 7, 4 }

code no      17:
================
1 1 1 1 1 0 0
2 1 1 0 0 1 0
3 1 1 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
3 0 0 0 
0 3 0 0 
0 0 3 0 
0 0 0 3 
, 1
, 
2 0 0 0 
0 2 0 0 
0 0 2 0 
2 2 2 2 
, 0
, 
1 0 0 0 
1 1 1 1 
0 0 0 1 
0 0 1 0 
, 1
, 
2 3 3 0 
0 1 0 0 
0 0 1 0 
2 2 2 2 
, 1
, 
2 1 1 0 
2 2 2 2 
0 0 0 2 
0 0 3 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(4, 5), 
(2, 5)(3, 4), 
(1, 6)(4, 5), 
(1, 6, 7)(2, 5)(3, 4)
orbits: { 1, 6, 7 }, { 2, 5, 4, 3 }

code no      18:
================
1 1 0 0 1 0 0
1 0 1 0 0 1 0
1 0 0 1 0 0 1
the automorphism group has order 96
and is strongly generated by the following 7 elements:
(
2 0 0 0 
0 2 0 0 
0 0 2 0 
0 0 0 2 
, 1
, 
3 0 0 0 
0 3 0 0 
0 0 3 0 
3 0 0 3 
, 1
, 
3 0 0 0 
0 3 0 0 
3 0 3 0 
0 0 0 3 
, 0
, 
2 0 0 0 
0 2 0 0 
2 0 0 2 
2 0 2 0 
, 0
, 
2 0 0 0 
2 2 0 0 
0 0 2 0 
0 0 0 2 
, 0
, 
1 0 0 0 
0 0 1 0 
0 1 0 0 
0 0 0 1 
, 1
, 
2 0 0 0 
2 0 0 2 
0 2 0 0 
2 0 2 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(4, 7), 
(3, 6), 
(3, 7)(4, 6), 
(2, 5), 
(2, 3)(5, 6), 
(2, 3, 7)(4, 5, 6)
orbits: { 1 }, { 2, 5, 3, 7, 6, 4 }

code no      19:
================
1 1 0 0 1 0 0
2 1 1 0 0 1 0
2 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 1 0 0 
0 0 1 0 
2 1 0 1 
, 0
, 
3 0 0 0 
0 3 0 0 
1 3 3 0 
0 0 0 3 
, 0
, 
2 0 0 0 
0 2 0 0 
0 0 0 2 
0 0 2 0 
, 0
, 
3 0 0 0 
3 3 0 0 
0 0 3 0 
0 0 0 3 
, 1
, 
0 1 0 0 
1 0 0 0 
0 0 2 0 
0 0 0 2 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(4, 7), 
(3, 6), 
(3, 4)(6, 7), 
(2, 5), 
(1, 2)
orbits: { 1, 2, 5 }, { 3, 6, 4, 7 }