The generator matrix

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

generates a code of length 42 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+73x^36+644x^37+1292x^38+2652x^39+3449x^40+5642x^41+5297x^42+5792x^43+3503x^44+2550x^45+989x^46+572x^47+200x^48+54x^49+35x^50+8x^51+4x^52+6x^53+3x^54+2x^56

The gray image is a code over GF(2) with n=336, k=15 and d=144.
This code was found by Heurico 1.16 in 5.79 seconds.