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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+96x^47+328x^48+432x^49+664x^50+798x^51+1274x^52+1202x^53+1200x^54+848x^55+568x^56+332x^57+168x^58+102x^59+86x^60+18x^61+48x^62+12x^63+14x^64+1x^80

The gray image is a code over GF(2) with n=424, k=13 and d=188.
This code was found by Heurico 1.16 in 0.959 seconds.