The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^34+122x^35+229x^36+500x^37+1104x^38+1824x^39+4967x^40+6642x^41+12023x^42+10554x^43+12213x^44+6562x^45+4915x^46+1870x^47+1080x^48+470x^49+183x^50+84x^51+65x^52+34x^53+25x^54+10x^55+4x^56+1x^68

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 30 seconds.