The generator matrix

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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+164x^35+440x^36+1062x^37+1647x^38+3452x^39+4204x^40+7640x^41+8462x^42+11046x^43+8662x^44+7978x^45+4453x^46+3350x^47+1325x^48+942x^49+402x^50+158x^51+80x^52+40x^53+11x^54+6x^55+6x^56+2x^57+2x^60+1x^62

The gray image is a code over GF(2) with n=344, k=16 and d=140.
This code was found by Heurico 1.16 in 40.9 seconds.