The generator matrix

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

generates a code of length 15 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+67x^6+250x^7+505x^8+1070x^9+2065x^10+3528x^11+5408x^12+7080x^13+8406x^14+8908x^15+8219x^16+7092x^17+5402x^18+3496x^19+2176x^20+1128x^21+439x^22+202x^23+75x^24+14x^25+5x^26

The gray image is a code over GF(2) with n=30, k=16 and d=6.
This code was found by Heurico 1.10 in 2.06 seconds.