The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  0  2  8  2  1  2  1  1  1  8 12  1  8  2  2  2  1  1  1  2  2  8  1
 0  2  0  2  0  0  2  6  4 10  4  6 14 12  4 10  6  4 10  0  2  2  0 14  6  6  6  0  4  8  2  8  2 14  4  6  2 10  6  0 12  2  0
 0  0  2  2  0  6  2  4  0  2  2  8 10  0  6 12 10 14 10  2  0  6  2  6 10  0 12  8  0  2 14  8  4 12 14  6  8 14  8  2  6  6  0
 0  0  0  4  0  0  0  0  0  0  0  0  0  0  8  8  8  8 12 12 12  4  4 12  8 12  4 12  4  8  0  4  8  4  0 12  4  4  4  4  8  0  0
 0  0  0  0 12  0  0  0  0  0 12 12  4  8 12 12  4  8  4  0 12  8 12  8  0  0  4  8 12  4  4  4  0  8  8  4  0 12  8  4  4  4  4
 0  0  0  0  0 12  8 12  4 12 12 12  0  0  0  0  4  4 12  4  8  8  4  0  8 12  4 12 12  0 12  0  8 12  8 12  0 12  8  8  4  0  4

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

Homogenous weight enumerator: w(x)=1x^0+56x^34+194x^35+503x^36+928x^37+1528x^38+2876x^39+4595x^40+7306x^41+9762x^42+10050x^43+9423x^44+7564x^45+4948x^46+2858x^47+1494x^48+716x^49+350x^50+204x^51+74x^52+60x^53+24x^54+10x^55+6x^56+2x^57+4x^58

The gray image is a code over GF(2) with n=344, k=16 and d=136.
This code was found by Heurico 1.16 in 43 seconds.