The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+129x^8+226x^9+519x^10+908x^11+1747x^12+2560x^13+3578x^14+4564x^15+4489x^16+4332x^17+3488x^18+2676x^19+1740x^20+928x^21+598x^22+172x^23+85x^24+18x^25+9x^26+1x^28

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 7.3 seconds.