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.