The generator matrix

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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+166x^56+112x^57+214x^58+504x^59+531x^60+1136x^61+650x^62+1624x^63+749x^64+1168x^65+346x^66+424x^67+258x^68+144x^69+58x^70+8x^71+64x^72+8x^74+18x^76+4x^78+4x^80+1x^92

The gray image is a code over GF(2) with n=504, k=13 and d=224.
This code was found by Heurico 1.16 in 2.29 seconds.