The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  0  1  2  1  1  2  1  1  8  1  1  4  2  1  1  2  1 12  1  8  1  4  2  1  1  1  1  2  2  1  2  2  1  2  1  1  2  1  4  1  1
 0  2  0  6  0  6  0  2  4  6 12 10 12  2  4 14  6  0 10  0 14  2  2 12 14  6  4  6  4 14  2  6  0  2  2 12  6 14  0  2 10  2  6  8 10 12 14 14  2 12  6  0 12 14 12 14  0 12  4 10 12 14  0
 0  0 12  0  0  4  4  4  4  0  8  4 12  8  0  4  0  0  8 12  4 12  0  8  8  0  8 12  8  4  4 12  8  8  4 12 12 12 12  4 12  0 12 12  8  0  0  8  0 12  0 12 12  8  8  8  8  0  8  8  4  0  0
 0  0  0 12 12  4  4  0  8  8  8  4 12 12  4  8  8  8  8  4  0  4  8  4  4 12  4  4  0  8  8  4  4 12  0  8  0  8  8 12  0  4  4 12  8  4  0  8  0  8  8  0  8  8 12  4  8  0 12  0 12  4  0
 0  0  0  0  8  0  0  0  8  8  8  0  8  0  0  0  8  0  8  8  8  8  0  8  8  8  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  0  0  0  8  8  0  8  0  8  0  0  0  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  0  0  8  0  8  8  8  8  0  0  0  8  8  8  0  8  0  8  0  0  8  0  8  0  0  8  8  0  8  0  8  8  8  8  8  8  8  8  0  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  0  8  0  0  8  0  8  8  8  0  8  0  0  0  8  8  8  0  0  0  8  8  0  0  0  8  0  8  8  8  0  0  8  0  8  8  8  8  0  8  8  8  0  8  8  0  0  0
 0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  8  8  0  0  8  8  0  0  8  0  0  8  0  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  8  0  8  8  8  0  0  0  0  8  0  8  0  8  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+35x^52+58x^53+173x^54+274x^55+451x^56+614x^57+940x^58+1646x^59+2420x^60+3314x^61+4243x^62+4478x^63+4210x^64+3532x^65+2344x^66+1590x^67+889x^68+580x^69+416x^70+168x^71+151x^72+84x^73+58x^74+36x^75+32x^76+8x^77+13x^78+3x^80+2x^81+2x^82+3x^86

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 21.3 seconds.