The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  8  1  1 10  1  1  2  4  1  1  1 12  1  2  1  1  2 10  2  1  1  1  1  2  1  1  2  2
 0  1 11  6  5  1 11  0  1  5  1  6 13  1  8  1  3  6  1  1  4  1  1  9 14  7  1  2  1  4 15  1  1  6  1 12  3  0  4  3  6  4  0
 0  0 12  0  0  0  0  4  4 12 12  0  8  8  8  0  8  4  4  4  4  0  4  4  4  0  0  8  4  0  8  4  4  0  8 12  4  0 12  4 12  8  0
 0  0  0 12  0  4  4  4 12 12  8  0  4  8  4  4  0  4 12  8  8  4  8  4  8  4  8 12  8 12  8  0 12 12 12  4  4  0  8 12  4  4  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  8  0  0  0  0  0  8  0  0  0  8  8  8  8  8  0  8  8  0  0  8  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  0  0  8  8  8  0  8  8  8  8  0  8  0  0  8
 0  0  0  0  0  0  8  0  8  0  0  8  0  8  8  0  8  0  0  0  8  8  0  8  0  8  8  0  8  8  0  0  8  8  8  0  0  8  0  0  0  8  8
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  8  0  0  8  0  8  8  0  0  8  0  8  8  0  0  8  8  0  8  8  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+122x^34+20x^35+429x^36+300x^37+1212x^38+2032x^39+4955x^40+7384x^41+10453x^42+11256x^43+11226x^44+7376x^45+4678x^46+2032x^47+1193x^48+296x^49+391x^50+20x^51+103x^52+4x^53+38x^54+11x^56+1x^58+2x^60+1x^66

The gray image is a code over GF(2) with n=344, k=16 and d=136.
This code was found by Heurico 1.16 in 29.6 seconds.