The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+164x^44+80x^45+470x^46+564x^47+1896x^48+2092x^49+4334x^50+3940x^51+5844x^52+3900x^53+4318x^54+2076x^55+1769x^56+580x^57+422x^58+76x^59+150x^60+4x^61+52x^62+27x^64+4x^66+2x^68+3x^72

The gray image is a code over GF(2) with n=416, k=15 and d=176.
This code was found by Heurico 1.16 in 10.7 seconds.