The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+64x^20+168x^21+419x^22+922x^23+1923x^24+4140x^25+7316x^26+11150x^27+13283x^28+11132x^29+7394x^30+4234x^31+1914x^32+852x^33+374x^34+138x^35+61x^36+28x^37+15x^38+4x^39+2x^40+2x^42

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 21.9 seconds.