The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+132x^46+276x^47+456x^48+568x^49+829x^50+1224x^51+1380x^52+1196x^53+763x^54+580x^55+332x^56+208x^57+119x^58+32x^59+64x^60+12x^61+9x^62+6x^64+4x^66+1x^80

The gray image is a code over GF(2) with n=416, k=13 and d=184.
This code was found by Heurico 1.16 in 0.997 seconds.