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

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

Homogenous weight enumerator: w(x)=1x^0+69x^34+98x^35+154x^36+228x^37+271x^38+458x^39+931x^40+1720x^41+2694x^42+3234x^43+2620x^44+1688x^45+980x^46+458x^47+255x^48+168x^49+133x^50+100x^51+66x^52+36x^53+12x^54+4x^55+5x^56+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 4.14 seconds.