The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+59x^36+214x^37+382x^38+572x^39+999x^40+1334x^41+1296x^42+1228x^43+907x^44+510x^45+345x^46+172x^47+76x^48+50x^49+24x^50+12x^51+6x^52+4x^53+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 0.742 seconds.