The generator matrix

 1  0  0  1  1  1  4 12  1  1  8  1  1 10  8  1  6  1  1 10  1  1  1 10  4  1  1  1  1  1 10  1  1  1  1  1 12  6  1  1  4  6
 0  1  0  0 13 11  1  1  7  1  1 14 10  8  1 13  0  4  1  1  6  3  4  1  1 11  8  5  2 13  1  3 13 12 10 12  1  6  4  5  0  1
 0  0  1  1 13  4  7  4  5  0  5  6 15  1  6 11  1  8  4  7  7 15 10  1  7  6  7  5  6  0 12  7  1  6  9 11 15  1  2 11  2 12
 0  0  0  2 10  0  8 10  4 14  6 10  0 14  0 12  8  6 12  4  6  2 14 12 14 14  0  8 14  8  0  4  4  4 10 10 12  6  2  8 10 14
 0  0  0  0  8  8  8  8  8  8  8  0  0  0  8  8  0  0  8  0  8  0  8  0  0  0  8  8  8  0  0  0  0  0  0  8  0  0  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+448x^36+1224x^37+2706x^38+4844x^39+7360x^40+10568x^41+11046x^42+10688x^43+7869x^44+4760x^45+2314x^46+1068x^47+434x^48+120x^49+58x^50+8x^51+15x^52+4x^54+1x^56

The gray image is a code over GF(2) with n=336, k=16 and d=144.
This code was found by Heurico 1.16 in 48.7 seconds.