The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+296x^34+598x^36+16x^37+1137x^38+416x^39+3348x^40+1776x^41+6860x^42+3776x^43+6926x^44+1776x^45+3522x^46+416x^47+1041x^48+16x^49+528x^50+235x^52+69x^54+10x^56+4x^58+1x^68

The gray image is a code over GF(2) with n=344, k=15 and d=136.
This code was found by Heurico 1.16 in 42.7 seconds.