The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+160x^32+394x^33+858x^34+1478x^35+2200x^36+3862x^37+4388x^38+5858x^39+4603x^40+4098x^41+2221x^42+1330x^43+722x^44+324x^45+174x^46+54x^47+18x^48+8x^49+7x^50+8x^52+2x^53

The gray image is a code over GF(2) with n=312, k=15 and d=128.
This code was found by Heurico 1.16 in 9.65 seconds.