The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+36x^8+92x^9+184x^10+290x^11+403x^12+630x^13+838x^14+1034x^15+1119x^16+1030x^17+878x^18+646x^19+468x^20+290x^21+146x^22+78x^23+20x^24+6x^25+2x^26+1x^28

The gray image is a code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.10 in 0.16 seconds.