the 1 isometry classes of irreducible [25,21,4]_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 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 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 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 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 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 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 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 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 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 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 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 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 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 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
1 0 4 1 0 0 0 0 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 0 0 0 0 4 0
0 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 1200
and is strongly generated by the following 4 elements:
(
2 0 0 0 
0 2 0 0 
2 0 4 4 
2 0 2 1 
, 
2 0 0 0 
0 2 4 1 
1 3 2 4 
4 1 2 4 
, 
2 0 0 0 
1 2 4 4 
0 0 0 2 
3 1 4 4 
, 
0 1 3 1 
4 4 4 4 
1 4 0 2 
3 3 1 0 
)
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, 22)(20, 21), 
(2, 23, 24, 25)(3, 6, 17, 20)(4, 10, 7, 22)(5, 19, 15, 18)(8, 9, 14, 16)(11, 21, 12, 13), 
(2, 11, 22, 8, 7, 17, 23, 20, 15, 16, 19, 21, 24, 12, 10, 14, 4, 3, 25, 6, 5, 9, 18, 13), 
(1, 12, 23, 16, 24, 5, 2, 19)(3, 14, 9, 13, 7, 11, 22, 10)(4, 6, 21, 17, 15, 18, 20, 8)
orbits: { 1, 19, 22, 5, 16, 2, 7, 11, 18, 6, 24, 9, 14, 15, 23, 25, 13, 10, 8, 17, 3, 4, 21, 20, 12 }