the 1 isometry classes of irreducible [20,17,3]_4 codes are:

code no       1:
================
1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
3 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
2 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
3 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 5760
and is strongly generated by the following 7 elements:
(
1 0 0 
0 1 0 
0 0 2 
, 1
, 
2 0 0 
0 1 0 
2 0 2 
, 1
, 
2 0 0 
0 1 0 
0 2 2 
, 0
, 
2 0 0 
1 0 2 
3 1 3 
, 0
, 
3 0 0 
2 2 1 
1 3 0 
, 0
, 
0 3 2 
1 2 2 
1 1 1 
, 1
, 
3 0 1 
2 3 1 
0 1 1 
, 0
)
acting on the columns of the generator matrix as follows (in order):
(4, 16)(6, 7)(8, 9)(11, 14)(12, 15)(13, 17)(19, 20), 
(3, 8)(4, 14)(5, 7)(11, 15)(12, 16)(13, 17)(18, 19), 
(3, 14, 11)(4, 8, 15)(5, 7, 6)(9, 16, 12)(10, 17, 13), 
(2, 17, 10)(3, 7, 15)(4, 12, 11)(5, 14, 9)(6, 16, 8), 
(2, 9, 16)(3, 17, 6)(4, 13, 11)(5, 10, 15)(7, 8, 14), 
(1, 18)(2, 12)(3, 4)(6, 15)(7, 10)(8, 17)(13, 14), 
(1, 17, 18, 13, 19, 10)(2, 20)(3, 15, 4, 6, 5, 11)(7, 8, 14)(9, 16)
orbits: { 1, 18, 10, 19, 17, 13, 5, 7, 20, 2, 3, 8, 4, 14, 6, 9, 15, 16, 12, 11 }