The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  0  3  2  1  1  2
 0  0  1  0  0  0  0  0  2  1  3  1  2  1  2
 0  0  0  1  0  0  0  0  3  1  1  0  2  2  1
 0  0  0  0  1  0  0  0  1  2  1  1  3  1  0
 0  0  0  0  0  1  0  1  0  3  2  3  1  3  2
 0  0  0  0  0  0  1  1  0  1  3  2  3  0  3
 0  0  0  0  0  0  0  2  2  0  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+74x^7+226x^8+448x^9+878x^10+1604x^11+2608x^12+3708x^13+4564x^14+4760x^15+4293x^16+3596x^17+2704x^18+1692x^19+920x^20+436x^21+172x^22+62x^23+16x^24+4x^25+2x^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 5.04 seconds.