the 1 isometry classes of irreducible [26,22,4]_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 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 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 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 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 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 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 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 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 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 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 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
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 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
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 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 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 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 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 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
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 0
3 3 4 1 0 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 31200
and is strongly generated by the following 9 elements:
(
4 0 0 0 
0 4 0 0 
0 0 4 0 
2 1 0 1 
, 
2 0 0 0 
0 2 0 0 
2 0 4 4 
2 0 2 1 
, 
3 0 0 0 
0 3 0 0 
1 4 1 4 
0 1 3 1 
, 
3 0 0 0 
0 4 0 0 
0 4 2 4 
1 1 3 2 
, 
2 0 0 0 
0 2 4 1 
1 3 2 4 
4 1 2 4 
, 
2 0 0 0 
0 3 4 3 
2 4 3 3 
0 4 3 2 
, 
2 0 0 0 
4 3 2 2 
2 0 2 1 
1 3 2 4 
, 
0 1 3 1 
4 4 4 4 
1 4 0 2 
3 3 1 0 
, 
2 2 1 4 
0 0 0 1 
1 4 0 2 
0 1 3 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 23)(10, 11)(12, 24)(13, 26)(14, 25)(15, 19)(16, 22)(17, 21)(18, 20), 
(3, 12)(4, 15)(5, 7)(6, 13)(8, 14)(9, 16)(10, 18)(11, 17)(19, 22)(20, 21), 
(3, 12, 24)(4, 16, 19)(5, 23, 7)(6, 13, 26)(8, 14, 25)(9, 15, 22)(10, 17, 20)(11, 18, 21), 
(3, 18, 23, 9, 14, 20, 6, 16, 24, 11, 5, 22, 8, 17, 26, 4, 12, 21, 7, 15, 25, 10, 13, 19), 
(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, 18, 24, 19)(3, 21, 17, 13)(4, 23, 7, 25)(5, 22, 15, 10)(6, 9, 20, 16)(8, 12, 14, 11), 
(2, 16, 25, 8, 24, 9, 23, 14)(3, 22, 21, 5, 17, 10, 13, 15)(4, 11, 19, 6, 7, 12, 18, 20), 
(1, 12, 23, 16, 24, 5, 2, 19)(3, 14, 9, 13, 7, 11, 22, 10)(4, 6, 21, 17, 15, 18, 20, 8), 
(1, 9, 15, 24, 16, 7, 10, 3, 22, 5, 19, 4, 2, 14, 13, 17, 6, 12, 18, 11, 21, 23, 8, 20, 25, 26)
orbits: { 1, 19, 26, 15, 22, 16, 13, 5, 24, 11, 2, 17, 25, 4, 9, 7, 3, 6, 14, 20, 23, 10, 12, 18, 21, 8 }