The generator matrix

 1  0  1  1  1 14  1  1  0  1  1  6  4  1  1  1  1  2  1  1  1  1 12 14  8 10  1  1  1  4  1  2  1  1  1  0  1  1  8  1  1  1
 0  1 11 14  5  1  0  3  1  6 13  1  1 12  7  9 10  1  1  2 15  4  1  1  1  1  6 14  2  1  0 14 13 14 11  1  6  3  2  5  3  0
 0  0 12  4  0  4 12  0 12  8 12  0 12  0 12  8  0 12  4  4  8  4  0  4  4  0  0  4 12 12  8  4  4 12 12  0  8  8  4  0  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  0  8  0  8  8  0  8  0  0  0  0  8  8  0  8  0  0  8  8  8  0  8  0  8  0
 0  0  0  0  8  0  0  0  0  8  0  8  8  0  8  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  0  0  0  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  0  8  8  0  8  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  8  0  8  8  0  8  0  8  8  8  0  0  8  0  0  8  0  0  0  0  8  8  8  0  0  8  0
 0  0  0  0  0  0  0  8  0  8  0  8  8  0  8  8  0  0  8  8  0  0  8  0  0  0  8  8  0  0  8  0  8  0  8  8  0  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  8  8  8  8  0  0  8  8  0  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+35x^32+64x^33+135x^34+256x^35+421x^36+666x^37+2833x^38+3538x^39+9792x^40+7800x^41+14555x^42+7704x^43+9780x^44+3532x^45+2831x^46+732x^47+405x^48+216x^49+109x^50+56x^51+37x^52+10x^53+15x^54+2x^55+6x^56+1x^58+2x^60+1x^62+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 26.5 seconds.