the 7 isometry classes of irreducible [21,17,4]_5 codes are:

code no       1:
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1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
1 0 0 0 
0 1 0 0 
1 2 3 3 
2 4 4 2 
, 
0 2 0 0 
3 0 0 0 
4 3 4 0 
0 0 0 4 
)
acting on the columns of the generator matrix as follows (in order):
(3, 14)(4, 16)(5, 6)(7, 13)(8, 12)(9, 15)(10, 17)(11, 18), 
(1, 2)(3, 7)(5, 12)(6, 8)(10, 11)(13, 14)(17, 18)(20, 21)
orbits: { 1, 2 }, { 3, 14, 7, 13 }, { 4, 16 }, { 5, 6, 12, 8 }, { 9, 15 }, { 10, 17, 11, 18 }, { 19 }, { 20, 21 }

code no       2:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 4
and is strongly generated by the following 1 elements:
(
3 0 1 1 
1 1 2 0 
0 2 1 2 
1 2 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 8, 2, 12)(3, 20, 14, 19)(4, 5, 17, 7)(6, 16, 13, 10)(9, 15, 18, 11)
orbits: { 1, 12, 2, 8 }, { 3, 19, 14, 20 }, { 4, 7, 17, 5 }, { 6, 10, 13, 16 }, { 9, 11, 18, 15 }, { 21 }

code no       3:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
2 0 0 0 
0 2 0 0 
2 0 4 4 
2 0 2 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 12)(4, 15)(5, 7)(6, 13)(8, 14)(9, 16)(10, 18)(11, 17)(19, 20)
orbits: { 1 }, { 2 }, { 3, 12 }, { 4, 15 }, { 5, 7 }, { 6, 13 }, { 8, 14 }, { 9, 16 }, { 10, 18 }, { 11, 17 }, { 19, 20 }, { 21 }

code no       4:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
0 4 0 0 
1 0 0 0 
4 2 2 0 
4 2 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(1, 2)(3, 6)(4, 9)(5, 14)(7, 8)(12, 13)(15, 16)(18, 21)
orbits: { 1, 2 }, { 3, 6 }, { 4, 9 }, { 5, 14 }, { 7, 8 }, { 10 }, { 11 }, { 12, 13 }, { 15, 16 }, { 17 }, { 18, 21 }, { 19 }, { 20 }

code no       5:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
4 3 1 1 
3 4 1 2 
2 3 3 1 
2 3 0 4 
)
acting on the columns of the generator matrix as follows (in order):
(1, 13)(2, 19)(3, 20)(4, 10)(5, 9)(6, 8)(7, 14)(11, 18)(12, 15)(16, 21)
orbits: { 1, 13 }, { 2, 19 }, { 3, 20 }, { 4, 10 }, { 5, 9 }, { 6, 8 }, { 7, 14 }, { 11, 18 }, { 12, 15 }, { 16, 21 }, { 17 }

code no       6:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
4 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
3 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 12
and is strongly generated by the following 2 elements:
(
2 0 0 0 
4 1 0 3 
4 4 2 3 
1 1 0 4 
, 
0 0 0 4 
1 1 0 4 
3 3 3 3 
4 1 0 3 
)
acting on the columns of the generator matrix as follows (in order):
(2, 10)(3, 21)(4, 11)(5, 8)(6, 15)(7, 19)(13, 17)(14, 18)(16, 20), 
(1, 11, 2, 9, 10, 4)(3, 7, 20, 18, 15, 5)(6, 14, 16, 19, 21, 8)(12, 17, 13)
orbits: { 1, 4, 11, 10, 2, 9 }, { 3, 21, 5, 19, 8, 15, 7, 16, 6, 18, 20, 14 }, { 12, 13, 17 }

code no       7:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
4 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
3 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 40
and is strongly generated by the following 3 elements:
(
3 0 0 0 
0 0 0 4 
0 2 3 4 
0 1 0 0 
, 
4 3 4 0 
4 4 2 3 
1 2 2 1 
2 1 4 3 
, 
0 2 3 4 
3 1 4 4 
3 1 3 0 
3 3 3 3 
)
acting on the columns of the generator matrix as follows (in order):
(2, 4)(3, 17)(6, 14)(7, 20)(8, 18)(9, 11)(12, 16)(13, 19), 
(1, 20, 9, 18, 4, 21, 2, 8, 11, 7)(3, 19, 6, 15, 14, 13, 17, 12, 5, 16), 
(1, 12, 8, 17)(2, 16, 20, 14)(3, 11, 15, 7)(4, 13, 18, 5)(6, 9, 19, 21)
orbits: { 1, 7, 17, 20, 11, 15, 3, 13, 8, 16, 9, 6, 19, 14, 4, 18, 2, 12, 5, 21 }, { 10 }