The generator matrix

 1  0  1  1  1  4  1  6  1  1 10  1  8 10  1  1  1  1 14  1
 0  1  1  0 11  1 10  1 13  7  1  0  2  1 10 10  1  4  1  0
 0  0  2  6  4  6  6  4  0  6  2  4  6 10  0  4 10 14  0  0
 0  0  0 12  0  4  8 12  4  4 12  4  4  0  0 12  8 12  4  8
 0  0  0  0  8  0  8  8  0  8  0  8  8  0  8  0  8  8  8  8
 0  0  0  0  0  8  0  8  0  8  0  8  0  8  8  8  8  0  0  8

generates a code of length 20 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+37x^14+120x^15+491x^16+1050x^17+3748x^18+5970x^19+9845x^20+6068x^21+3858x^22+1004x^23+375x^24+114x^25+68x^26+10x^27+7x^28+1x^30+1x^32

The gray image is a code over GF(2) with n=160, k=15 and d=56.
This code was found by Heurico 1.16 in 2.18 seconds.