The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  2  0  0
 0  1  0  0  0  0  0  2  2  2  0  1  0  1  1  1  1
 0  0  1  0  0  0  0  0  1  2  3  0  1  2  3  1  0
 0  0  0  1  0  0  0  0  1  3  3  3  2  1  1  1  2
 0  0  0  0  1  0  0  1  0  3  2  2  1  2  2  1  3
 0  0  0  0  0  1  0  1  0  0  1  3  2  0  3  1  2
 0  0  0  0  0  0  1  1  3  0  0  3  1  2  3  3  1

generates a code of length 17 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+320x^10+1068x^12+2570x^14+4131x^16+4394x^18+2578x^20+1006x^22+284x^24+30x^26+2x^28

The gray image is a code over GF(2) with n=34, k=14 and d=10.
This code was found by Heurico 1.16 in 45.4 seconds.