The generator matrix

 1  1  1  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  1  1  1  1  1  1  4  1  1  0  1  2  1  2  8  1  2  2  1  1
 0  2  0  6  4 14 12  2  0  6 12 10  8 14  0  6  2  4 12 14  2  6  0  6  8 10  4  2 10 14  8  6  0  4  2  4 12  4  2  6  6  0  2  2 12  6 14 10 10
 0  0 12  0  4  4  8  4  0  8  0  0  4  4 12 12  4  4  4  4  4  0  8 12  4  8  0  4 12 12  0  8  4  0  8 12  4  4  8  4  0 12 12 12 12  0 12  4  4
 0  0  0  8  0  0  8  0  0  8  8  0  0  8  0  8  8  8  8  8  8  8  8  0  8  0  0  0  0  8  0  0  8  8  8  0  0  8  0  0  0  8  0  8  0  8  0  8  0
 0  0  0  0  8  0  0  8  8  8  8  8  0  8  8  0  8  8  0  8  0  8  0  0  8  8  0  8  8  0  8  0  0  8  0  0  8  8  0  8  0  0  8  0  0  0  8  8  0
 0  0  0  0  0  8  0  8  0  0  0  0  8  0  8  0  8  0  0  8  8  8  8  0  8  8  8  0  0  8  8  8  8  8  8  0  8  8  0  0  0  0  8  0  0  0  0  0  8

generates a code of length 49 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+159x^44+176x^45+412x^46+320x^47+472x^48+1056x^49+528x^50+320x^51+318x^52+176x^53+80x^54+54x^56+19x^60+4x^62+1x^80

The gray image is a code over GF(2) with n=392, k=12 and d=176.
This code was found by Heurico 1.16 in 7.04 seconds.