The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  6  1  1  1  0  1  1  1  1  1 12 10  0  1  1  0  1  1  6  1  1  1  1  1  1  1  0  0  0
 0  1  3  6  5  1 12  7  1 10  9  1  6  1  3  0  5  1 12 15 10  9  3  1  1  1  0  5  1  6 15  1 12  9 10 12  3  3  0  1  1  1
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  8  8  8  8  0  8  8  0  0  8  8  0  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  0  8  8  8  8  0  8  0  8  8  8  8  0  8  0  8  8  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  8  0  0  8  8  0  0  8  8  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  8  0  0  0  0  0  8  8  8  0  0  0  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  8  8  8  8  0  0  8  8  0  8  0  0  0  0  0  0  0  0  8  8  8  0  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  8  8  0  0  8  0  0  8  0  8  0  8  0  0  0  8  8  8  0  0  0  8  8  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  8  0  0  0  8  8  0  8  0  0  0  0  0  0  8  0  8  0  8
 0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  0  8  8  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  0  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+106x^32+96x^34+64x^35+642x^36+576x^37+1696x^38+5056x^39+6694x^40+12736x^41+10240x^42+12736x^43+6664x^44+5056x^45+1696x^46+576x^47+632x^48+64x^49+96x^50+82x^52+22x^56+4x^60+1x^64

The gray image is a code over GF(2) with n=336, k=16 and d=128.
This code was found by Heurico 1.16 in 26.2 seconds.