The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+88x^49+205x^50+300x^51+274x^52+328x^53+314x^54+272x^55+122x^56+96x^57+38x^58+4x^59+2x^60+2x^62+1x^66+1x^80

The gray image is a code over GF(2) with n=424, k=11 and d=196.
This code was found by Heurico 1.16 in 0.121 seconds.