the 10 isometry classes of irreducible [7,4,3]_4 codes are:

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

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

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

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

code no       5:
================
1 1 1 1 0 0 0
1 1 0 0 1 0 0
1 0 1 0 0 1 0
0 1 1 0 0 0 1
the automorphism group has order 336
and is strongly generated by the following 7 elements:
(
1 0 0 
0 1 0 
0 0 1 
, 1
, 
3 0 0 
0 3 0 
0 3 3 
, 1
, 
3 0 0 
0 3 0 
3 0 3 
, 1
, 
2 0 0 
0 0 2 
0 2 0 
, 0
, 
3 0 0 
3 0 3 
3 3 0 
, 1
, 
0 0 3 
3 3 3 
3 0 0 
, 0
, 
0 3 3 
0 3 0 
3 3 0 
, 0
)
acting on the columns of the generator matrix as follows (in order):
id, 
(3, 7)(4, 6), 
(3, 6)(4, 7), 
(2, 3)(5, 6), 
(2, 6)(3, 5), 
(1, 3)(2, 4), 
(1, 7)(3, 5)
orbits: { 1, 3, 7, 6, 2, 5, 4 }

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

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

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

code no       9:
================
1 1 1 1 0 0 0
1 1 0 0 1 0 0
3 2 1 0 0 1 0
2 3 1 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
2 0 0 
0 2 0 
0 0 2 
, 1
, 
3 0 0 
0 3 0 
3 3 3 
, 1
, 
2 0 0 
0 2 0 
1 3 2 
, 0
, 
3 3 3 
0 0 3 
0 3 0 
, 0
, 
2 3 1 
3 2 1 
0 0 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(6, 7), 
(3, 4), 
(3, 6)(4, 7), 
(1, 4)(2, 3), 
(1, 7)(2, 6)
orbits: { 1, 4, 7, 3, 6, 2 }, { 5 }

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