The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  2  1  4  1  1  1  4  0  1  1  1  1  1  1  2  1  2  1
 0 12  0  4  0  0  4  4  8  8  4 12 12 12  0  8  8  4  8  4  0  4 12  0  4 12  4 12  0  0 12  4  4  0  8  0  4  4  4  4 12  0
 0  0 12  4  0 12 12  0  8  4  4  0  8  4  8 12  4  4  4  0  0  4  8  4 12 12 12  4  0  4  8  8  4  4  0  0  0 12 12  0  8  0
 0  0  0  8  0  0  8  0  0  0  0  8  8  0  8  8  8  0  8  8  8  0  8  0  0  8  0  8  8  8  8  0  8  0  0  0  0  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  8  8  0  8  0  0  0  8  0  0  8  8  8  8  0  8  8  0  8  0  0  8  0  8  8  0
 0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  8  0  0  0  8  0  0  0  8  8  0  0  0  8  8  8  0  8  8  8  0  0  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+30x^36+36x^37+51x^38+126x^39+167x^40+488x^41+299x^42+486x^43+164x^44+100x^45+11x^46+26x^47+15x^48+16x^49+17x^50+2x^51+6x^52+5x^54+1x^56+1x^70

The gray image is a code over GF(2) with n=336, k=11 and d=144.
This code was found by Heurico 1.16 in 0.105 seconds.