The generator matrix

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

generates a code of length 17 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+46x^13+72x^14+66x^15+69x^16+44x^17+56x^18+52x^19+24x^20+38x^21+32x^22+10x^23+2x^24

The gray image is a code over GF(2) with n=34, k=9 and d=13.
This code was found by Heurico 1.10 in 7.66 seconds.