The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  1  2  0  1  2  1  4  2  1  1  1  1  1  2  1  2  1  1  1  2  2  2  8  1  1  1
 0  2  0 14  4  6 12  2  0  6  8 10  4 14  2 12 14  2  6  2  0 10  6  2  2  8  2 10  2 12 14 12  2  4 14 14  8  8  4  4  8 14  0
 0  0 12  4  4  0  0  4  0  8 12  8  4 12  4  8  4  4  0  0  0  8  8  4  4 12  4  0 12  0 12  0 12 12  4  8 12 12 12  4  8 12  0
 0  0  0  8  0  0  0  0  8  8  8  8  0  8  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  0  0  8  0  8  8  8  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  0  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  8  0  8  8  8  0  8  8  0  8  0  0  0  0  8  8  0  8  8  8  0  8  0  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  0  0  0  8  8  0  8  0  8  0  8  8  8  8  0  0  0  8  8  8  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  8  8  0  8  0  8  8  0  0  8  0  8  8  8  8  8  8  8  0  0  0  8  8  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+33x^34+16x^35+200x^36+132x^37+504x^38+468x^39+1192x^40+1652x^41+2676x^42+2628x^43+2775x^44+1676x^45+1160x^46+444x^47+375x^48+124x^49+211x^50+28x^51+56x^52+23x^54+8x^56+1x^60+1x^70

The gray image is a code over GF(2) with n=344, k=14 and d=136.
This code was found by Heurico 1.16 in 3.28 seconds.