The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  4  1  2  2  1  1  4  4  1  1
 0 12  0  0  0  0  0  0  0 12  4 12 12  4  8 12  4 12 12  8  4  8  4  4  4  8  0  0
 0  0 12  0  0  0  4 12  4  4  4  8  0  8  8  0  0 12  4  0  4 12 12 12  4  8  4  0
 0  0  0 12  0  4  4  4  8  4  0 12  4  8  8  8  4  0  8  0  4 12  4  4  4 12  0  0
 0  0  0  0 12  4  0  4  4  8  0  8 12  4  0  8  8  0  4 12 12  8 12  8 12  0 12  8
 0  0  0  0  0  8  0  0  8  0  8  8  8  0  8  8  0  0  0  0  8  8  8  0  8  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  0  8  0  8  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+57x^20+82x^21+172x^22+232x^23+337x^24+586x^25+2402x^26+1148x^27+6337x^28+1142x^29+2411x^30+612x^31+388x^32+222x^33+119x^34+52x^35+42x^36+16x^37+13x^38+4x^39+6x^40+3x^42

The gray image is a code over GF(2) with n=224, k=14 and d=80.
This code was found by Heurico 1.16 in 2.05 seconds.