The generator matrix

 1  0  1  1  1  6  1  1  0  1  1 14  1  1  1  0 12  1  1  1  1  1  2  6  4  1  1  1
 0  1 11  6  1  1  8  5  1  3  0  1 11  6  0  1  1 15  6  8 13 12  4  1  4  8  0  0
 0  0 12  0  0  0  0  0  0  0  0  8  8 12  4 12  4 12 12 12  8  0 12  8  4  8  0  0
 0  0  0 12  0  0  0  0  4  4 12 12 12  4  4 12  8  8  0  4  0  8  8  8  0  8  0  0
 0  0  0  0  4  0  8  4  0  4  8  8 12  0 12  4  4  8 12  4  8 12  4  4  4 12  8  0
 0  0  0  0  0 12 12  4 12  8 12  8 12  8 12 12  8 12  8  8 12  4 12 12 12  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+95x^20+168x^21+323x^22+662x^23+1563x^24+3146x^25+7610x^26+12322x^27+13603x^28+12490x^29+7601x^30+3262x^31+1558x^32+558x^33+311x^34+134x^35+74x^36+22x^37+24x^38+4x^39+2x^40+3x^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 15.5 seconds.