The generator matrix

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

generates a code of length 15 over Z4 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+50x^7+163x^8+308x^9+513x^10+832x^11+1285x^12+1810x^13+2159x^14+2200x^15+2084x^16+1766x^17+1297x^18+904x^19+551x^20+270x^21+125x^22+46x^23+12x^24+6x^25+2x^26

The gray image is a code over GF(2) with n=30, k=14 and d=7.
This code was found by Heurico 1.10 in 0.416 seconds.