The generator matrix

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

generates a code of length 16 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+149x^8+214x^9+576x^10+738x^11+1824x^12+2616x^13+3496x^14+4696x^15+4307x^16+4500x^17+3464x^18+2604x^19+1824x^20+856x^21+632x^22+152x^23+87x^24+6x^25+24x^26+2x^27

The gray image is a code over GF(2) with n=32, k=15 and d=8.
This code was found by Heurico 1.16 in 7.27 seconds.