The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  1 12  1  2  1  2  1  1  1  2  1  1  2 12  1  1  1  1  8  1  1  1
 0  2  0  6  4 14 12  2  0  6 12  8 10 14  0 12  6 14  2  6  2  2  2  2  6 10  8  2 12 14  4 14 10  2  4  2  4  4  2  0 12  0
 0  0 12  0  4  4  0  4  0  8  0 12  8 12  8 12  4 12  0  8  4  8  4 12  0  8  4  0  0 12 12 12  8  0 12  4 12  0 12  0  8  0
 0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  8  8  8  8  8  8  8  0  8  0  8  8  0  8  0  8  8  0  8  0  8  8
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  0  8  0  8  8  0  0  8  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  8  0  0  0
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  0  8  0  8  0  0  8  0  0  8  8  8  8  8  0  8  0  8  8  8  0  8  0  8  8  8  8
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8  0  8  8  8  8  8  8  0  0  8  0  0  8  8  0  8  0  8  0  0  8  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+181x^36+64x^37+412x^38+384x^39+1187x^40+1088x^41+1632x^42+1088x^43+1143x^44+384x^45+368x^46+64x^47+144x^48+16x^50+27x^52+4x^54+3x^56+1x^60+1x^64

The gray image is a code over GF(2) with n=336, k=13 and d=144.
This code was found by Heurico 1.16 in 3.52 seconds.