The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+149x^10+485x^12+792x^14+1161x^16+978x^18+378x^20+128x^22+22x^24+1x^26+1x^28

The gray image is a code over GF(2) with n=32, k=12 and d=10.
This code was found by Heurico 1.16 in 0.295 seconds.