The generator matrix
1 0 0 1 1 1 2 1 1 0 1 0 2 1 1 2 1
0 1 0 2 1 3 1 0 1 1 0 2 1 3 3 2 1
0 0 1 1 3 2 1 2 1 2 3 1 3 3 1 2 2
generates a code of length 17 over Z4 who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+45x^16+16x^20+2x^24
The gray image is a code over GF(2) with n=34, k=6 and d=16.
This code was found by Heurico 1.16 in 0.00468 seconds.