The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^34+12x^35+100x^36+64x^37+179x^38+144x^39+708x^40+704x^41+1536x^42+1224x^43+1537x^44+704x^45+698x^46+144x^47+161x^48+64x^49+69x^50+12x^51+42x^52+19x^54+10x^56+6x^58+1x^60+1x^66

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 1.35 seconds.