the 4 isometry classes of irreducible [9,4,5]_4 codes are:

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

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

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

code no       4:
================
1 1 1 1 1 1 0 0 0
2 2 1 1 0 0 1 0 0
2 1 2 0 1 0 0 1 0
0 2 1 2 1 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
2 0 0 0 0 
0 0 0 1 0 
0 0 2 0 0 
3 3 2 2 0 
1 1 1 1 1 
, 0
, 
2 0 0 0 0 
0 2 3 2 3 
0 0 2 0 0 
3 3 3 3 3 
1 1 2 2 0 
, 1
, 
0 0 0 0 2 
2 2 2 2 2 
0 2 0 0 0 
2 0 0 0 0 
0 0 0 2 0 
, 0
, 
1 1 1 1 1 
0 0 0 0 1 
0 0 0 1 0 
0 0 1 0 0 
0 1 0 0 0 
, 1
, 
0 3 1 3 1 
1 1 1 1 1 
2 2 3 3 0 
0 0 3 0 0 
0 0 0 1 0 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(2, 7, 4)(5, 9, 6), 
(2, 9)(4, 6)(5, 7), 
(1, 4, 5)(2, 3, 6), 
(1, 6)(2, 5)(3, 4), 
(1, 6, 2, 7, 3, 4, 5, 9)
orbits: { 1, 5, 6, 9, 7, 4, 2, 3 }, { 8 }