The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+144x^47+471x^48+882x^49+1440x^50+1766x^51+2527x^52+2250x^53+2499x^54+1680x^55+1203x^56+700x^57+445x^58+174x^59+81x^60+66x^61+29x^62+12x^63+5x^64+6x^65+3x^66

The gray image is a code over GF(2) with n=424, k=14 and d=188.
This code was found by Heurico 1.16 in 3.02 seconds.