The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^10+78x^11+217x^12+206x^13+297x^14+416x^15+420x^16+618x^17+481x^18+472x^19+329x^20+194x^21+171x^22+56x^23+55x^24+6x^25+13x^26+2x^27+2x^28

The gray image is a code over GF(2) with n=34, k=12 and d=10.
This code was found by Heurico 1.10 in 0.078 seconds.