the 2 isometry classes of irreducible [9,2,4]_2 codes are:

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

code no       2:
================
1 1 1 0 0 0 0 1 0
1 1 0 1 1 1 1 0 1
the automorphism group has order 960
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 1 0 
1 1 0 1 1 1 1 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 1 0 0 
1 1 0 1 1 1 1 
0 0 0 0 0 1 0 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
0 0 0 1 0 0 0 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
0 0 0 0 1 0 0 
, 
1 0 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 1 
0 0 0 0 1 0 0 
0 0 0 0 0 1 0 
0 0 0 1 0 0 0 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
0 0 1 0 0 0 0 
1 1 0 1 1 1 1 
0 0 0 0 1 0 0 
0 0 0 0 0 1 0 
0 0 0 0 0 0 1 
, 
1 0 0 0 0 0 0 
0 1 0 0 0 0 0 
1 1 1 0 0 0 0 
0 0 0 0 0 0 1 
0 0 0 0 0 1 0 
0 0 0 0 1 0 0 
0 0 0 1 0 0 0 
, 
1 1 1 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 0 0 0 1 0 0 
0 0 0 0 0 0 1 
0 0 0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(7, 9), 
(6, 7), 
(6, 7, 9), 
(5, 7), 
(4, 7), 
(4, 9), 
(3, 8)(4, 7)(5, 6), 
(1, 3, 2, 8)(4, 7, 6)
orbits: { 1, 8, 3, 2 }, { 4, 7, 9, 6, 5 }