The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+49x^54+80x^55+233x^56+314x^57+536x^58+896x^59+1039x^60+1768x^61+2282x^62+2138x^63+2254x^64+1748x^65+1035x^66+856x^67+469x^68+288x^69+183x^70+52x^71+52x^72+34x^73+31x^74+8x^75+12x^76+8x^77+10x^78+2x^79+4x^80+1x^82+1x^90

The gray image is a code over GF(2) with n=504, k=14 and d=216.
This code was found by Heurico 1.16 in 5.77 seconds.