The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  4 10  1  1  1  1  6  1  4  1  1  4  1  1  1 14  4  1  1  6  1  6  1  1  1  1  8  0 12  1  1  1  1  1  6  1  1  8  1  1  1  2  0  1  1  0  8  1  1 12  1  1  2  1  8  6 10  4  1  1  1
 0  1  1  0  3  1  5  4  1  8  3  1  1 10 15  2 13  1 11  1  2 14  1  1  9 14  1  1  3 12  1 15  1 15 10  4  9  1  1  1  5  3  1 10  2  1  6 15  1  7  4 15  6  8  5 11  8  1  6 13  1 12  2  6 15  1  1  1  2 14 14  0
 0  0  2  0  0  0  2 10  6  2  8 14  0  8  2 10  4 12 14 14  6  4 10 12  6  4  2 12 14  0 14 12  2 10  4  6  4  8  2  0  0 12 10  0  2  8  2  6 14 14  8 12  6 12  4  6  2 12  8  0 10  8  0  4  4  4  6 14  2  2 12  0
 0  0  0  2  0  2  2  8 14 14  6  4  6 14 10  6  2 12  8 10  4  0  0  8  8  6  6  0 14  6  0 12 10 12 12  8  4 12 12 14 14  2 14  8  0 10 14 14  2 12  0  0  0  2  6  2  2  4 12  4  8  2  2  2  8  6 10  2  0  6  6  0
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  0  0  8  8  0  8  8  8  8  0  8  8  8  0  0  0  8  8  0  0  8  0  0  0  0  0  8  8  8  0  8  0  0  8  8  0  8  0  8  0  0  0  8  8  8  0  0  0  8  8  8  0  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  8  8  0  0  8  0  8  0  8  8  8  0  8  0  8  8  0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  8  0  8  0  8  8  0  0  8  0  0  0  8

generates a code of length 72 over Z16 who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+38x^63+335x^64+736x^65+1334x^66+2338x^67+3761x^68+4694x^69+6841x^70+8166x^71+8807x^72+8780x^73+7102x^74+4584x^75+3298x^76+2110x^77+1336x^78+574x^79+348x^80+170x^81+78x^82+38x^83+25x^84+20x^85+11x^86+6x^87+1x^88+2x^89+2x^90

The gray image is a code over GF(2) with n=576, k=16 and d=252.
This code was found by Heurico 1.16 in 54.8 seconds.