The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+168x^47+489x^48+872x^49+1490x^50+1750x^51+2247x^52+2690x^53+2092x^54+1706x^55+1331x^56+792x^57+420x^58+172x^59+71x^60+26x^61+28x^62+10x^63+15x^64+4x^65+2x^66+2x^67+6x^68

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 2.76 seconds.