The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  4  2  1  4  2  2  1  2  2  2  1  1  1  2  1  1  1  1
 0 12  0  4  0  0  4 12  0  0 12 12  0  8 12  8 12  0  4 12 12 12  4  4 12  8  8  0  4 12  8  4 12  0  4  4  4 12  4 12  8 12
 0  0 12  4  0 12  4  0  0 12 12  8  8 12  4  4  0  8  4 12  0  0  4  4  0  4  8 12  4  8  4 12  0 12  8  0 12  0 12  0  8 12
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  0  0  8  8  8  8  8  0  0  8  0  8  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  0  8  8  0  0  0  8  8  0  0  8  8  0  0  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  8  8  0  0  0  8  8  8  0  0  8  8  0  8  0  8  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  8  0  8  8  0
 0  0  0  0  0  0  0  8  0  0  8  0  8  8  0  0  8  0  0  8  8  0  0  0  0  8  0  8  8  0  8  8  0  8  0  0  8  0  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  0  0  8  8  0  0  8  0  8  0  8  0  8  8  0  8  8  8  8  8  0  0
 0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  8  0  0  8  0  8  0  8  8  8  8  8  0  8  8

generates a code of length 42 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+204x^32+4x^33+276x^34+52x^35+775x^36+256x^37+1076x^38+672x^39+3337x^40+5160x^41+9056x^42+5160x^43+3462x^44+672x^45+1120x^46+256x^47+723x^48+52x^49+236x^50+4x^51+177x^52+12x^54+23x^56+1x^60+1x^76

The gray image is a code over GF(2) with n=336, k=15 and d=128.
This code was found by Heurico 1.16 in 18.8 seconds.