The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  2  1  1  0  2  1  1  0  2  1  2  1  1  4  1  1  2  1  1  1  1  1  2  2  1  4  8  0  1  2  8  8  2
 0  2  0  6  4  6 12  2  6 14  8 12  0  4  2 10 14  4  2 14  2  0  2  6 14  4  2 14 14  2 10  8  2  2  8 10 12 12  0  6  6 14  2  6  4  2  4  2  0  2  0 14
 0  0 12  0  4  0  0  8  4 12  0  4  4  8 12 12  0  8  4  4  8  0 12  4  8  0  0  8 12  0  8  0  4  4  0  8  8 12 12 12  0  0  4  4  8  8  4 12 12  0  4  8
 0  0  0 12  0  0  0 12  4  8 12 12  4 12  8 12  8  8  8  8  4  8  4  4  4 12  0 12  8  4  8 12  0  8  4  0  8 12  4 12  8 12  8 12 12  4  0  8  4 12 12  4
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  8  0  8  8  0  8  8  8  8  8  0  0  8  8  8  8  8  0  8  0  8  8  8  8  8  8  8  0  0  0  0  8
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  8  0  8  8  0  8  8  8  0  0  8  0  0  0  8  0  8  8  8  0  8  8  0  8  8  8  0  0  8  0  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  8  8  8  8  0  8  0  0  8  0  8  8  0  0  0  0  0  8  0  8  8  0  8  0  0  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+118x^44+84x^45+428x^46+440x^47+960x^48+1052x^49+1928x^50+2024x^51+2521x^52+1940x^53+1820x^54+1160x^55+881x^56+372x^57+324x^58+88x^59+156x^60+8x^61+40x^62+29x^64+4x^66+5x^68+1x^72

The gray image is a code over GF(2) with n=416, k=14 and d=176.
This code was found by Heurico 1.16 in 4.55 seconds.