The generator matrix

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

generates a code of length 15 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+130x^8+114x^9+313x^10+320x^11+688x^12+1032x^13+912x^14+1152x^15+917x^16+1052x^17+698x^18+320x^19+312x^20+104x^21+120x^22+2x^25+5x^26

The gray image is a code over GF(2) with n=30, k=13 and d=8.
This code was found by Heurico 1.10 in 0.164 seconds.