The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^7+214x^8+468x^9+917x^10+1616x^11+2596x^12+3632x^13+4460x^14+4820x^15+4465x^16+3624x^17+2606x^18+1632x^19+916x^20+464x^21+204x^22+58x^23+4x^25+5x^26

The gray image is a code over GF(2) with n=30, k=15 and d=7.
This code was found by Heurico 1.16 in 11.1 seconds.