The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+161x^20+304x^22+32x^23+972x^24+320x^25+2752x^26+2016x^27+6106x^28+7552x^29+5824x^30+2016x^31+3083x^32+320x^33+768x^34+32x^35+386x^36+80x^38+40x^40+2x^44+1x^52

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 7.31 seconds.