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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+56x^53+111x^54+174x^55+259x^56+326x^57+383x^58+652x^59+1096x^60+1604x^61+2286x^62+2628x^63+2221x^64+1652x^65+1152x^66+576x^67+332x^68+252x^69+181x^70+146x^71+101x^72+62x^73+41x^74+44x^75+19x^76+16x^77+6x^78+4x^79+2x^80+1x^92

The gray image is a code over GF(2) with n=504, k=14 and d=212.
This code was found by Heurico 1.16 in 7.14 seconds.