the 1 isometry classes of irreducible [19,16,3]_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
1 1 0 0 1 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
3 1 0 0 0 0 1 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
2 0 1 0 0 0 0 0 1 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 1 1 0 0 0 0 0 0 0 1 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
3 1 1 0 0 0 0 0 0 0 0 0 1 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
1 2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 576
and is strongly generated by the following 8 elements:
(
3 0 0 
0 2 0 
0 0 3 
, 1
, 
2 0 0 
0 3 0 
0 1 2 
, 1
, 
2 0 0 
0 1 0 
0 2 2 
, 0
, 
3 0 0 
0 3 0 
3 0 3 
, 0
, 
1 0 0 
3 0 1 
2 2 2 
, 1
, 
2 0 0 
0 1 2 
0 0 3 
, 1
, 
0 3 2 
1 2 2 
1 1 1 
, 1
, 
3 1 3 
2 0 1 
2 0 3 
, 1
)
acting on the columns of the generator matrix as follows (in order):
(4, 15)(5, 7)(9, 10)(11, 14)(12, 17)(13, 16), 
(3, 14)(5, 6)(8, 15)(9, 17)(10, 16)(12, 13), 
(3, 14, 11)(4, 8, 15)(5, 7, 6)(9, 16, 12)(10, 17, 13), 
(3, 8)(4, 11)(9, 10)(12, 13)(14, 15)(16, 17)(18, 19), 
(2, 17, 11, 9)(3, 7, 14, 4)(5, 15, 12, 10)(6, 16, 13, 8), 
(2, 14)(4, 13)(5, 15)(6, 17)(7, 16)(8, 9), 
(1, 18)(2, 12)(3, 4)(6, 15)(7, 10)(8, 17)(13, 14), 
(1, 18, 19)(2, 16, 5, 8, 14, 10)(3, 11, 7, 6, 13, 9)(4, 17, 12)
orbits: { 1, 18, 19 }, { 2, 9, 14, 12, 10, 17, 11, 8, 13, 3, 15, 7, 16, 6, 4, 5 }