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

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

Homogenous weight enumerator: w(x)=1x^0+72x^34+94x^35+147x^36+292x^37+422x^38+698x^39+1273x^40+1774x^41+2138x^42+2500x^43+2303x^44+1788x^45+1201x^46+700x^47+402x^48+208x^49+146x^50+94x^51+62x^52+32x^53+20x^54+10x^55+4x^56+2x^57+1x^62

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 4.19 seconds.