The generator matrix

 1  0  1  1  1  6  1  1  0  1 14  1  1  1  0  1 14  1  1 12  1  1  8  1 14  1  1  1  1 10 12  1  1  1  1  2 12  1  1  1  1  2  1
 0  1 11  6  1  1  8  5  1  3  1  6 11  0  1  5  1 14  9  1  6  3  1 12  1 13  6  0  5  1  1 10 11  3  0  0  1  3 13  2  0  8  0
 0  0 12  0  0  0  0  0  0  0  0  8  8  4 12 12  4 12 12  4 12  4  0  8  8 12  4  0 12  0  8  4  4 12  8  0  8  8 12  0 12  0  0
 0  0  0 12  0  0  0  0  4  4 12 12 12 12 12  8 12 12  4  8  0  4 12  0 12  8  8  4  0  8  4  0  8  4  4  8  8  8  8  8  4  4  0
 0  0  0  0  4  0  8  4  0  4  0  0  4 12  4  8 12 12  0  4  4  8  8  8  4 12  8 12 12  4 12  8  4 12  4 12  4  0  0 12 12 12  0
 0  0  0  0  0 12 12  4 12  8  8  4 12 12  4  4  0  8  8  8  8  0  8  8  4  4  4  0  8 12  0 12  4  8  4  8  0  8  0  8  4  4  8

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

Homogenous weight enumerator: w(x)=1x^0+49x^34+150x^35+271x^36+458x^37+947x^38+2260x^39+4212x^40+7398x^41+10935x^42+12162x^43+10916x^44+7566x^45+4165x^46+2210x^47+949x^48+410x^49+228x^50+104x^51+65x^52+40x^53+24x^54+10x^55+2x^56+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 30.4 seconds.