The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+164x^36+92x^37+686x^38+1100x^39+2145x^40+2392x^41+3332x^42+2392x^43+2073x^44+1100x^45+612x^46+92x^47+135x^48+36x^50+18x^52+6x^54+7x^56+1x^60

The gray image is a code over GF(2) with n=336, k=14 and d=144.
This code was found by Heurico 1.16 in 3.52 seconds.