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

generates a code of length 44 over Z16 who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+156x^34+478x^36+12x^37+831x^38+388x^39+1707x^40+1836x^41+3868x^42+3908x^43+6332x^44+3908x^45+3950x^46+1836x^47+1801x^48+388x^49+758x^50+12x^51+396x^52+154x^54+35x^56+10x^58+2x^60+1x^70

The gray image is a code over GF(2) with n=352, k=15 and d=136.
This code was found by Heurico 1.16 in 16.1 seconds.