The generator matrix

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

generates a code of length 29 over Z16 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+84x^21+177x^22+554x^23+1028x^24+2086x^25+3795x^26+7208x^27+10900x^28+13818x^29+10879x^30+7384x^31+3770x^32+2090x^33+965x^34+464x^35+200x^36+98x^37+24x^38+6x^39+4x^40+1x^48

The gray image is a code over GF(2) with n=232, k=16 and d=84.
This code was found by Heurico 1.16 in 21.8 seconds.