The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+150x^47+289x^48+478x^49+675x^50+968x^51+857x^52+1418x^53+948x^54+1058x^55+477x^56+348x^57+249x^58+148x^59+49x^60+26x^61+24x^62+12x^63+5x^64+2x^65+7x^66+2x^68+1x^74

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 1.08 seconds.