The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^36+124x^38+363x^40+256x^41+980x^42+512x^43+1019x^44+256x^45+260x^46+155x^48+44x^50+31x^52+9x^56+1x^60+1x^68

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 0.366 seconds.