The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2  1 12  1  1  1  1  2  0  1  2 12  2  0  1  1  1  2  1  2  1  1  4  1  2  1
 0  2 12  6  0  6 12 10  0  6 12 10  6  2  0  6 10 12  2 10  0  6  6  6  2 12 10  2 10  2  0 10  6  6 12  6 12  0 12  6  0  6
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  8  8  0  0  8  8  0  8  0  0  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  0  8  0  8  0  8  8  8  0  8  8  0  8  8  0  8  0  0  8  8  0  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  8  8  0  8  8  0  0  0  0  8  0  0  0  8  0  0  8  8  0  8  8  0  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  0  0  0  8  0  8  0  8  0  0  0  0  0  8  0  8  8  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  0  0  0  8  8  8  0  0  0  8  8  8  0  0  0  8  8  8
 0  0  0  0  0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  8  8  0  8  8  8  0  8  0  8  0  0  0  0  0  8  0  0  8  8  0  8  8
 0  0  0  0  0  0  0  0  0  8  0  8  8  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  8  8  8  0  8  0  0  0  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+132x^32+8x^33+92x^34+40x^35+639x^36+320x^37+1552x^38+1792x^39+4619x^40+3984x^41+6440x^42+3984x^43+4615x^44+1792x^45+1552x^46+320x^47+599x^48+40x^49+92x^50+8x^51+117x^52+25x^56+5x^60

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 11.6 seconds.