The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  0  1  2  1  1  2  8  1  1  2  1 12  1  4  1  2  1  1  2  1  2  1  0  1  2  1  1 12  1  2  1  1  2  1  2  1  2  8  1  1
 0  2  0  6  4  6 12  2  6 14  8 12  0  2 10 12  0  6  4 14  6  2  8  2 10  6 10 12 14  2 10 14 10 12  2  4  2  0 10  6 14  2  6 10 14  2  0 10 12  4  2  4  6 14  0 10 10  4  6 12  2  2  0
 0  0 12  0  4  0  0  8  4 12  0  4  4  4  4  0  8  0  0  8 12  4 12  4 12  0  8 12  0  0  4  4 12  4 12  4  8  8  4  8  0 12 12  8 12  0 12  0  8 12  0  0 12  8  8  0  8 12 12  4  8  0  0
 0  0  0 12  0  0  0 12  4  8 12 12  4  0 12 12  8  0  4 12  4  8  8  4 12  8  0  4  4  4  0  8  4  8 12 12 12  4  4  4  8  8  4  0 12  8 12 12  4 12  8  8 12  4  0  0  0  8  4  0 12 12  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  8  0  0  8  8  8  8  0  8  0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  0  8  0  8  0  8  0  0  8  8  8  0  0  0
 0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  8  0  0  8  0  0  0  8  0  8  0  8  0  8  0  8  0  8  8  0  0  8  0  8  0  8  8  0  0  8  0  0  0  8  8  0  8  8  8  8  8  8  0  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  0  8  8  8  8  8  0  8  0  8  8  8  0  0  8  8  0  0  0  8  8  8  0  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  0  0  8  8  8  0  8  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+38x^54+110x^55+285x^56+236x^57+608x^58+700x^59+1362x^60+1526x^61+2401x^62+2018x^63+2306x^64+1590x^65+1322x^66+702x^67+569x^68+170x^69+189x^70+40x^71+67x^72+54x^73+36x^74+14x^75+12x^76+8x^77+11x^78+5x^80+2x^82+1x^84+1x^86

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 5.8 seconds.