The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  2  2  2  2  2  2  1  1  4  1  1  4  2
 0 12  0  0  0  4 12  4  0  8  0 12 12  4  4  8  4 12  8  0  4  4  0  4 12  0  0  0  0
 0  0 12  0  4  4 12  0  0  0  4 12  4  8  4  0  0  8  4  4  4  8  0  0  8 12  4  4  0
 0  0  0 12  4  0 12  4  0  4 12  4 12  8  0  4 12  8  8 12  0  4  0  0  0  4  0 12  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  0  0  8  0  0  8  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  0  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  0  8  0  8  0  8  8  8  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  8  8  0  8  0  8  8  0  8  0  0  8
 0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+124x^20+407x^22+48x^23+887x^24+256x^25+1867x^26+1968x^27+6900x^28+7680x^29+7015x^30+2064x^31+1941x^32+256x^33+834x^34+16x^35+360x^36+105x^38+27x^40+11x^42+1x^46

The gray image is a code over GF(2) with n=232, k=15 and d=80.
This code was found by Heurico 1.16 in 7.45 seconds.