The generator matrix

 1  0  1  1  1 14  1  1  0  1  1  6  1 12  2  1  1  1  1  1  1 14  1  6  0  8  1  1
 0  1 11 14  5  1  0  3  1  6 13  1  4  1  1 15  1  2  7  8 11  1 14  1  1  2  3  0
 0  0 12  4  0  4 12  0 12  8 12  0 12  0 12  0  4  4  4 12 12 12  4  8  0  4  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  8  0  0  8  0  8  8  0
 0  0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  0  8  8  8  0  8  8  0  0  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  0  0  0  8  8  0  0  8  0  8
 0  0  0  0  0  0  0  8  0  8  0  8  8  8  0  0  8  8  8  0  0  0  0  8  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  0  8  0  0  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+119x^20+312x^22+128x^23+1766x^24+2176x^25+9284x^26+11008x^27+15938x^28+11008x^29+9300x^30+2176x^31+1776x^32+128x^33+300x^34+103x^36+4x^38+8x^40+1x^48

The gray image is a code over GF(2) with n=224, k=16 and d=80.
This code was found by Heurico 1.16 in 13.4 seconds.