The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  4 10  1  1  1  4  1  1  4  1 14  1  1  1  1  0 14  1  8  1  1  2  1  1 12  1  1  1  1  0  2  0  1  0  4  1  2  1  1  1  1
 0  1  1  0  3  1  5  4  1  8  3  1  1 10 15  2  1  3  9  1 12  1  2  6 15  9  1  1  0  1 14 13  8 13  4  1  9  6 13 10  1  1  2  6  2  2  7  8 11 15  6  0
 0  0  2  0  0  0  2 10  6  2  8 14  0  8  2  6 14 14 12 10 12  8 10  8  4  4  6 10  6 10  4 12 10 10  4  0  8 14  2 10  4  2 14  0 10  8 14  4 10  4  4 12
 0  0  0  2  0  2  2  8 14 14  6  4  6 14 10  4 10  8  2  0 12 12  6  8  2 12  0  6  6  6 14  8 14 10 14 14  6  8 12  2  2  4 12  4  6  2  2  2  8  4  4  4
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  0  8  8  0  8  0  8  0  0  0  0  8  0  8  0  0  8  8  8  0  0  8  0  8  0  8  8  8  0  8  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  8  0  0  8  8  0  0  0  0  8  8  8  0  8  8  0  0  8  0  8  0  8  0  0  0  0  8

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+104x^44+320x^45+949x^46+1386x^47+3328x^48+4934x^49+7443x^50+9340x^51+10089x^52+9230x^53+7684x^54+4796x^55+3169x^56+1334x^57+814x^58+332x^59+157x^60+50x^61+35x^62+18x^63+14x^64+4x^65+3x^66+2x^68

The gray image is a code over GF(2) with n=416, k=16 and d=176.
This code was found by Heurico 1.16 in 35.9 seconds.