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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+45x^54+84x^55+97x^56+144x^57+225x^58+222x^59+279x^60+628x^61+1466x^62+2010x^63+1391x^64+614x^65+250x^66+174x^67+166x^68+94x^69+85x^70+58x^71+37x^72+50x^73+35x^74+12x^75+11x^76+6x^77+4x^78+2x^80+1x^82+1x^98

The gray image is a code over GF(2) with n=504, k=13 and d=216.
This code was found by Heurico 1.16 in 1.8 seconds.