The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+65x^36+216x^37+383x^38+594x^39+921x^40+1260x^41+1419x^42+1286x^43+894x^44+512x^45+288x^46+158x^47+93x^48+60x^49+21x^50+10x^51+5x^52+5x^56+1x^62

The gray image is a code over GF(2) with n=336, k=13 and d=144.
This code was found by Heurico 1.16 in 0.772 seconds.