the 21 isometry classes of irreducible [7,4,3]_5 codes are:

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

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

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

code no       4:
================
1 1 1 4 0 0 0
1 1 0 0 4 0 0
2 1 0 0 0 4 0
0 2 1 0 0 0 4
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 }

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

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

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

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

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

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

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

code no      12:
================
1 1 1 4 0 0 0
1 1 0 0 4 0 0
2 0 1 0 0 4 0
1 2 1 0 0 0 4
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 }

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

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

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

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

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

code no      18:
================
1 1 1 4 0 0 0
1 1 0 0 4 0 0
3 2 1 0 0 4 0
4 3 1 0 0 0 4
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
1 0 0 
0 1 0 
1 2 4 
, 
1 1 1 
0 0 4 
0 4 0 
, 
0 1 0 
1 0 0 
4 4 4 
)
acting on the columns of the generator matrix as follows (in order):
(3, 7)(4, 6), 
(1, 4)(2, 3), 
(1, 2)(3, 4)(6, 7)
orbits: { 1, 4, 2, 6, 3, 7 }, { 5 }

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

code no      20:
================
1 1 1 4 0 0 0
2 1 0 0 4 0 0
3 1 0 0 0 4 0
4 1 0 0 0 0 4
the automorphism group has order 40
and is strongly generated by the following 3 elements:
(
2 0 0 
0 2 0 
3 3 3 
, 
1 0 0 
2 3 0 
0 0 3 
, 
4 3 0 
3 4 0 
0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4), 
(2, 6, 5, 7), 
(1, 5, 2, 6)
orbits: { 1, 6, 2, 7, 5 }, { 3, 4 }

code no      21:
================
1 1 1 4 0 0 0
2 1 0 0 4 0 0
3 1 0 0 0 4 0
2 2 1 0 0 0 4
the automorphism group has order 8
and is strongly generated by the following 2 elements:
(
4 0 0 
0 4 0 
2 2 1 
, 
4 3 0 
3 4 0 
0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(3, 7), 
(1, 5, 2, 6)
orbits: { 1, 6, 2, 5 }, { 3, 7 }, { 4 }