the 1 isometry classes of irreducible [10,1,10]_4 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1
the automorphism group has order 7257600
and is strongly generated by the following 16 elements:
(
2 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 
0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 2 0 0 
0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 0 0 2 
, 1
, 
3 0 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 0 
0 0 0 3 0 0 0 0 0 
0 0 0 0 3 0 0 0 0 
0 0 0 0 0 3 0 0 0 
0 0 0 0 0 0 3 0 0 
0 0 0 0 0 0 0 3 0 
3 3 3 3 3 3 3 3 3 
, 0
, 
1 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 0 
, 1
, 
3 0 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 0 
0 0 0 3 0 0 0 0 0 
0 0 0 0 3 0 0 0 0 
0 0 0 0 0 3 0 0 0 
0 0 0 0 0 0 3 0 0 
3 3 3 3 3 3 3 3 3 
0 0 0 0 0 0 0 0 3 
, 0
, 
2 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 
0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 0 0 2 
0 0 0 0 0 0 0 2 0 
0 0 0 0 0 0 2 0 0 
, 1
, 
3 0 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 0 
0 0 0 3 0 0 0 0 0 
0 0 0 0 3 0 0 0 0 
0 0 0 0 0 0 3 0 0 
0 0 0 0 0 0 0 3 0 
0 0 0 0 0 3 0 0 0 
0 0 0 0 0 0 0 0 3 
, 0
, 
1 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 1 1 1 
0 0 0 0 0 0 1 0 0 
0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 1 
, 1
, 
1 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 1 0 
, 0
, 
2 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 
0 0 2 0 0 0 0 0 0 
0 0 0 2 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 0 2 
0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 2 0 0 
0 0 0 0 2 0 0 0 0 
, 1
, 
3 0 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 0 
0 0 0 0 3 0 0 0 0 
0 0 0 3 0 0 0 0 0 
0 0 0 0 0 3 0 0 0 
0 0 0 0 0 0 3 0 0 
0 0 0 0 0 0 0 0 3 
0 0 0 0 0 0 0 3 0 
, 1
, 
3 0 0 0 0 0 0 0 0 
0 3 0 0 0 0 0 0 0 
0 0 0 0 0 3 0 0 0 
0 0 0 0 0 0 3 0 0 
0 0 0 3 0 0 0 0 0 
0 0 3 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 3 
0 0 0 0 0 0 0 3 0 
0 0 0 0 3 0 0 0 0 
, 1
, 
1 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 
0 0 0 0 0 1 0 0 0 
0 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 0 
, 1
, 
2 0 0 0 0 0 0 0 0 
0 2 0 0 0 0 0 0 0 
2 2 2 2 2 2 2 2 2 
0 0 0 0 0 0 0 2 0 
0 0 0 2 0 0 0 0 0 
0 0 0 0 2 0 0 0 0 
0 0 0 0 0 2 0 0 0 
0 0 0 0 0 0 2 0 0 
0 0 2 0 0 0 0 0 0 
, 0
, 
1 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 
0 0 0 0 1 0 0 0 0 
0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 1 0 0 
0 1 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 
, 0
, 
0 0 0 0 0 0 0 0 3 
0 3 0 0 0 0 0 0 0 
0 0 0 0 0 3 0 0 0 
0 0 0 3 0 0 0 0 0 
0 0 0 0 3 0 0 0 0 
3 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 3 0 0 
0 0 3 0 0 0 0 0 0 
0 0 0 0 0 0 0 3 0 
, 0
, 
3 3 3 3 3 3 3 3 3 
0 0 0 0 0 0 0 3 0 
0 0 0 0 0 0 0 0 3 
0 0 0 0 0 3 0 0 0 
0 3 0 0 0 0 0 0 0 
0 0 0 3 0 0 0 0 0 
0 0 0 0 0 0 3 0 0 
3 0 0 0 0 0 0 0 0 
0 0 3 0 0 0 0 0 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
id, 
(9, 10), 
(8, 9), 
(8, 10), 
(7, 9), 
(6, 8, 7), 
(6, 8, 10), 
(5, 8, 9, 7, 6), 
(5, 9, 6, 7, 8, 10), 
(4, 5)(8, 9), 
(3, 6)(4, 5, 9, 7), 
(3, 6, 5, 7, 9, 8, 4), 
(3, 9, 10)(4, 5, 6, 7, 8), 
(2, 8, 3, 9, 6)(4, 5), 
(1, 6, 3, 8, 9), 
(1, 8, 2, 5, 10)(3, 9)(4, 6)
orbits: { 1, 9, 10, 8, 7, 5, 3, 6, 2, 4 }