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

generates a code of length 43 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+42x^36+72x^37+77x^38+148x^39+149x^40+128x^41+246x^42+2380x^43+233x^44+120x^45+155x^46+156x^47+82x^48+64x^49+33x^50+4x^51+5x^52+1x^74

The gray image is a code over GF(2) with n=344, k=12 and d=144.
This code was found by Heurico 1.16 in 0.306 seconds.