The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+317x^48+304x^49+806x^50+880x^51+1274x^52+1216x^53+1130x^54+896x^55+791x^56+272x^57+170x^58+16x^59+88x^60+6x^62+18x^64+6x^68+1x^72

The gray image is a code over GF(2) with n=424, k=13 and d=192.
This code was found by Heurico 1.16 in 10.9 seconds.