The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  2  2  4  2  2  1  2  0  8  0  2  1  4  1  1  0  2  2  1  4  2  2
 0 12  0  0  0  0  0  0  0 12 12  4  4  4  4  4  0 12  4  8  0  8  0  4  8  4 12  0  8  8  4  4 12 12 12  4  0  8  8  0  0 12 12  4  0  8 12  4  8  8  4  0  8  0  0 12  4 12  4  0  4  4 12
 0  0 12  0  0  0  4 12  4  4 12  8  4  8  8  4  0  4 12 12  4  8  8 12  8  0  0 12  8 12 12  0  0 12 12  8  0  8  0  0  4 12  8  0 12  4 12 12  8  0  8  4  8 12  8  4 12  8  4 12  0  8  8
 0  0  0 12  0  4  4 12  0  8 12 12 12 12  8  0 12  0  4  0  0  4  8 12  4  8 12 12  8  4  8 12  0  4  4  8 12 12 12  4 12 12  4  0  4  8  8  4  0  4  0 12 12  0  8  4 12  0  0  4  8  8  8
 0  0  0  0 12  4  0 12  4 12  8  4 12  8 12  0  4  4  0 12  0  0  8 12  0 12  8  4  4  0  8 12  0  8 12  0  8 12  4  4  0  8  4 12 12  0 12 12  4 12  8  8  4  8  8  4  0  0  8 12 12  4  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  8  0  0  0  0  0  0  0  8  8  0  0  0  8  8  8  0  8  0  8  8  8  8  0  8  8  8  8  8  0  8  0  0  8  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  0  0  8  8  8  0  0  8  0  8  8  8  8  8  8  0  0  8  8  8  8  0  8  8  0  8  0  8  8  8  8  0  0  0  0  8  0  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  0  0  0  8  8  8  8  8  0  8  8  8  0  8  0  8  8  0  0  8  8  0  0  8  0  8  0  0  8  8  0  0  0  8  0  0  8  8  0  0

generates a code of length 63 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+149x^52+507x^54+32x^55+810x^56+164x^57+1271x^58+912x^59+2849x^60+2640x^61+4683x^62+4752x^63+4712x^64+2680x^65+2817x^66+944x^67+1288x^68+144x^69+762x^70+16x^71+349x^72+4x^73+173x^74+73x^76+23x^78+7x^80+3x^82+1x^84+1x^86+1x^88

The gray image is a code over GF(2) with n=504, k=15 and d=208.
This code was found by Heurico 1.16 in 27.1 seconds.