The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1  4  1  2  1  2  1  1  1  1  2  1  1  1  8  2
 0 12  0  0  0  0  0  0  0  4 12 12  4  8 12  8  4  8 12 12  8  4  8  8  8  4 12  8 12 12  0  0  4 12  0  0  4  8 12  4  8  4
 0  0 12  0  0  8 12 12  4  4  4  8  4  4 12  4  0  0 12  4  8  8  8  4  4  8  8 12  8  4  0  0 12 12 12  8  4  4  4 12  4  8
 0  0  0 12  0 12 12  4  8  0  0  0  4 12  4  4 12  8 12  8  8  4 12  0  4  4  0  8  4  4  8  0  4  8  0  8 12 12  0  0  0 12
 0  0  0  0 12  4  8  4  4  0  4  4  4  8  0 12  0 12 12 12  4 12  8 12  8  0 12 12  4  8 12  4  4  0 12  4 12  0 12 12 12  0

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

Homogenous weight enumerator: w(x)=1x^0+130x^36+4x^37+214x^38+84x^39+283x^40+1192x^41+350x^42+1192x^43+248x^44+84x^45+160x^46+4x^47+87x^48+38x^50+17x^52+6x^54+1x^56+1x^68

The gray image is a code over GF(2) with n=336, k=12 and d=144.
This code was found by Heurico 1.16 in 0.317 seconds.