the 4 isometry classes of irreducible [22,18,4]_5 codes are:

code no       1:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
1 0 0 0 
0 1 0 0 
1 2 3 3 
2 4 4 2 
, 
2 0 0 0 
0 2 0 0 
2 0 4 4 
2 0 2 1 
, 
2 0 0 0 
0 3 0 0 
1 2 1 0 
4 4 0 1 
, 
0 2 0 0 
3 0 0 0 
4 3 4 0 
0 0 0 4 
)
acting on the columns of the generator matrix as follows (in order):
(3, 14)(4, 16)(5, 6)(7, 13)(8, 12)(9, 15)(10, 17)(11, 18), 
(3, 12)(4, 15)(5, 7)(6, 13)(8, 14)(9, 16)(10, 18)(11, 17)(19, 22)(20, 21), 
(3, 6, 8, 7)(4, 10, 9, 11)(5, 12, 13, 14)(15, 18, 16, 17)(19, 20, 22, 21), 
(1, 2)(3, 7)(5, 12)(6, 8)(10, 11)(13, 14)(17, 18)(20, 21)
orbits: { 1, 2 }, { 3, 14, 12, 7, 8, 13, 5, 6 }, { 4, 16, 15, 11, 9, 18, 17, 10 }, { 19, 22, 21, 20 }

code no       2:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
2 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
0 1 4 2 
0 2 1 2 
1 3 2 4 
2 3 3 1 
, 
2 2 2 2 
2 1 1 0 
4 4 0 1 
4 3 2 2 
)
acting on the columns of the generator matrix as follows (in order):
(1, 17)(2, 19)(3, 20)(4, 21)(5, 9)(6, 7)(8, 16)(10, 15)(11, 22)(12, 18)(13, 14), 
(1, 5)(2, 6)(3, 11)(4, 14)(7, 19)(8, 18)(9, 17)(12, 16)(13, 21)(20, 22)
orbits: { 1, 17, 5, 9 }, { 2, 19, 6, 7 }, { 3, 20, 11, 22 }, { 4, 21, 14, 13 }, { 8, 16, 18, 12 }, { 10, 15 }

code no       3:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
3 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 24
and is strongly generated by the following 3 elements:
(
2 0 0 0 
0 2 0 0 
2 4 1 1 
4 3 3 4 
, 
4 0 0 0 
3 3 1 0 
0 1 4 2 
3 1 1 3 
, 
3 0 1 1 
1 1 2 0 
0 2 1 2 
1 2 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 14)(4, 16)(5, 6)(7, 13)(8, 12)(9, 15)(10, 17)(11, 18)(21, 22), 
(2, 12, 8)(3, 5, 17)(4, 20, 16)(6, 14, 10)(7, 13, 19)(9, 11, 22)(15, 21, 18), 
(1, 8, 2, 12)(3, 20, 14, 19)(4, 5, 17, 7)(6, 16, 13, 10)(9, 15, 18, 11)
orbits: { 1, 12, 8, 2 }, { 3, 14, 17, 19, 6, 20, 10, 5, 13, 4, 7, 16 }, { 9, 15, 22, 11, 18, 21 }

code no       4:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
2 4 1 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
0 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
3 4 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
1 4 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
3 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
2 0 0 0 
0 2 0 0 
2 0 4 4 
2 0 2 1 
, 
2 0 0 0 
0 2 0 0 
4 4 3 0 
1 3 0 3 
, 
0 1 0 0 
3 0 0 0 
2 3 0 4 
3 1 3 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 12)(4, 15)(5, 7)(6, 13)(8, 14)(9, 16)(10, 18)(11, 17)(19, 20), 
(3, 8)(4, 9)(5, 13)(6, 7)(10, 11)(12, 14)(15, 16)(17, 18)(19, 20)(21, 22), 
(1, 2)(3, 11, 8, 10)(4, 6, 9, 7)(5, 16, 13, 15)(12, 18, 14, 17)(19, 22, 20, 21)
orbits: { 1, 2 }, { 3, 12, 8, 10, 14, 17, 11, 18 }, { 4, 15, 9, 7, 16, 13, 6, 5 }, { 19, 20, 21, 22 }