The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^44+60x^45+400x^46+708x^47+1349x^48+2380x^49+3634x^50+5044x^51+5512x^52+5044x^53+3544x^54+2380x^55+1303x^56+708x^57+292x^58+60x^59+134x^60+56x^62+18x^64+10x^66+4x^68+1x^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.