The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+69x^36+80x^38+225x^40+512x^41+288x^42+512x^43+214x^44+80x^46+57x^48+5x^52+4x^56+1x^72

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 0.111 seconds.