the 1 isometry classes of irreducible [10,5,5]_3 codes are:

code no       1:
================
1 1 1 1 1 2 0 0 0 0
2 2 1 1 0 0 2 0 0 0
2 1 2 0 1 0 0 2 0 0
0 2 2 1 1 0 0 0 2 0
1 2 0 2 1 0 0 0 0 2
the automorphism group has order 720
and is strongly generated by the following 6 elements:
(
2 0 0 0 0 
0 2 0 0 0 
2 1 0 1 2 
2 2 2 2 2 
0 1 1 2 2 
, 
1 0 0 0 0 
0 2 0 0 0 
2 2 1 1 0 
0 2 2 1 1 
0 0 0 1 0 
, 
1 0 0 0 0 
0 2 0 0 0 
0 0 0 1 0 
1 2 0 2 1 
1 2 1 0 2 
, 
1 0 0 0 0 
0 0 0 2 0 
2 1 2 0 1 
0 0 2 0 0 
0 2 2 1 1 
, 
2 0 0 0 0 
0 2 2 1 1 
2 2 2 2 2 
0 0 0 0 2 
2 1 2 0 1 
, 
1 1 1 1 1 
0 1 1 2 2 
1 0 0 0 0 
0 0 2 0 0 
1 1 2 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 10)(4, 6)(5, 9)(7, 8), 
(3, 8, 10, 7)(4, 5, 6, 9), 
(3, 6, 10, 4)(5, 7, 9, 8), 
(2, 8, 3, 4)(5, 6, 7, 9), 
(2, 6, 3, 9)(4, 7, 8, 5), 
(1, 3, 4, 6)(2, 7, 5, 9)
orbits: { 1, 6, 4, 5, 3, 2, 9, 10, 8, 7 }