The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  8  1  2  1  1  2  8  1  1  4  2  1  1  1  4  2  2
 0  2  0  6  0  6  0  2  4  6  6  2 12  6 10  4 10  2 14 12  2 12  2  6  4  8 14  8
 0  0 12  0  0  4  4  4  4  0  8  0  8 12  4  0  4 12  4 12 12  4 12  8  8  4 12  8
 0  0  0 12 12  4  4  0  8  8  8  4  0 12  4  4 12  0  0  4  8  4  0  0  4  0  0 12
 0  0  0  0  8  0  0  0  8  8  0  8  8  8  0  8  0  0  0  8  8  0  8  0  0  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  8  8  0  8
 0  0  0  0  0  0  8  0  0  8  8  8  0  8  8  0  8  0  8  0  0  0  0  0  8  8  8  0
 0  0  0  0  0  0  0  8  8  8  8  0  8  8  0  8  8  8  8  0  8  8  8  0  8  8  8  0

generates a code of length 28 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+56x^20+132x^21+194x^22+526x^23+736x^24+2246x^25+2881x^26+7310x^27+4557x^28+7358x^29+2888x^30+2298x^31+739x^32+482x^33+166x^34+106x^35+50x^36+22x^37+14x^38+4x^40+1x^42+1x^44

The gray image is a code over GF(2) with n=224, k=15 and d=80.
This code was found by Heurico 1.16 in 5.96 seconds.