the 1 isometry classes of irreducible [4,1,4]_25 codes are:

code no       1:
================
1 1 1 4
the automorphism group has order 48
and is strongly generated by the following 6 elements:
(
8 0 0 
0 8 0 
0 0 8 
, 1
, 
4 0 0 
0 4 0 
1 1 1 
, 0
, 
10 0 0 
0 0 10 
0 10 0 
, 1
, 
24 0 0 
6 6 6 
0 24 0 
, 1
, 
0 0 2 
0 2 0 
2 0 0 
, 0
, 
23 23 23 
0 0 7 
0 7 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
id, 
(3, 4), 
(2, 3), 
(2, 3, 4), 
(1, 3), 
(1, 4)(2, 3)
orbits: { 1, 3, 4, 2 }