the 1 isometry classes of irreducible [23,19,4]_5 codes are:

code no       1:
================
1 1 1 1 4 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
1 2 1 0 0 0 4 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
2 1 0 1 0 0 0 0 4 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
4 4 0 1 0 0 0 0 0 0 4 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
4 3 1 1 0 0 0 0 0 0 0 0 4 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
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 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 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 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 1 3 1 0 0 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 0 0 4 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
1 4 3 1 0 0 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 0 0 4
the automorphism group has order 12
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 
, 
1 0 0 0 
1 0 4 1 
0 1 3 1 
4 2 3 1 
, 
0 4 0 0 
4 0 0 0 
4 3 2 2 
0 4 1 3 
, 
3 0 2 3 
3 0 0 0 
0 2 3 4 
2 4 1 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, 22)(20, 21), 
(2, 23)(3, 19)(4, 20)(5, 9)(6, 13)(7, 16)(8, 11)(10, 18)(12, 22)(14, 17)(15, 21), 
(1, 2)(3, 14)(4, 17)(5, 7)(6, 13)(8, 12)(9, 18)(10, 16)(11, 15)(19, 20)(21, 22), 
(1, 2, 23)(3, 20, 17)(4, 19, 14)(5, 18, 16)(7, 10, 9)(8, 15, 22)(11, 12, 21)
orbits: { 1, 2, 23 }, { 3, 12, 19, 14, 17, 22, 8, 11, 20, 4, 21, 15 }, { 5, 7, 9, 16, 18, 10 }, { 6, 13 }