The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+236x^47+849x^48+1652x^49+2783x^50+4016x^51+4436x^52+5110x^53+4657x^54+3790x^55+2458x^56+1414x^57+821x^58+328x^59+94x^60+68x^61+23x^62+10x^63+10x^65+4x^66+4x^67+2x^68+2x^69

The gray image is a code over GF(2) with n=424, k=15 and d=188.
This code was found by Heurico 1.16 in 8.06 seconds.