The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+18x^34+50x^35+78x^36+114x^37+158x^38+236x^39+299x^40+1160x^41+482x^42+3038x^43+482x^44+1162x^45+296x^46+218x^47+132x^48+110x^49+58x^50+40x^51+22x^52+12x^53+10x^54+2x^55+7x^56+2x^57+2x^58+2x^60+1x^64

The gray image is a code over GF(2) with n=344, k=13 and d=136.
This code was found by Heurico 1.16 in 1.03 seconds.