The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  1  6  1  1 12  1  1  1  1  1  0  1  1  2
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  5  1  6 15  1  9  3  0  5  0  1  3  5  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  8  0  0  0  0  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  0  8  8  8  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  0  8  0  8  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  8  8  0  0  0  0  8  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  0  8  0  8  0  0  8  8  8  0  0  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  0  8  8  0  0  8  0  8  0

generates a code of length 29 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+102x^20+90x^22+96x^23+662x^24+1216x^25+2208x^26+10144x^27+9287x^28+18048x^29+9028x^30+10144x^31+2487x^32+1216x^33+432x^34+96x^35+225x^36+18x^38+34x^40+1x^44+1x^52

The gray image is a code over GF(2) with n=232, k=16 and d=80.
This code was found by Heurico 1.16 in 12.7 seconds.