The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+78x^32+114x^33+235x^34+310x^35+537x^36+882x^37+1245x^38+2256x^39+3464x^40+4768x^41+5219x^42+4216x^43+3538x^44+2672x^45+1290x^46+780x^47+475x^48+254x^49+185x^50+114x^51+90x^52+14x^53+17x^54+4x^55+6x^56+1x^58+2x^60+1x^68

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 14.7 seconds.