The generator matrix

 1  1  1  1  1  1  1  1  2  0  1  1  1  2  1 12  1  0  1  1  1  2  2  1  1  2  2  1  1
 0  2 12  6  0  6 12 10  6  2  0  6 12 10 10  2  0  2 12  6 10  6  6  0  6  0  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  8  0  0  8  0  8  0  0  8  8  8  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  0  0  0  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  0  0  0  8  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  8  8  0  8  0  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  8  0  8  8  0  0  0  0  8  8  8  8  0  8  8  0  0  0  0  0
 0  0  0  0  0  0  0  0  8  8  0  0  0  8  0  8  0  8  0  0  0  8  8  8  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+80x^20+102x^22+16x^23+420x^24+224x^25+968x^26+1264x^27+4091x^28+2112x^29+3988x^30+1264x^31+1075x^32+224x^33+296x^34+16x^35+195x^36+22x^38+24x^40+1x^44+1x^52

The gray image is a code over GF(2) with n=232, k=14 and d=80.
This code was found by Heurico 1.16 in 1.52 seconds.