The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+273x^36+676x^37+1095x^38+2478x^39+3736x^40+5264x^41+5791x^42+5486x^43+3534x^44+2340x^45+1147x^46+530x^47+259x^48+96x^49+25x^50+18x^51+5x^52+8x^53+6x^54

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 7.34 seconds.