The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+138x^64+480x^65+1362x^66+2448x^67+3773x^68+4830x^69+7363x^70+7794x^71+9241x^72+8194x^73+7239x^74+4800x^75+3715x^76+1982x^77+1131x^78+540x^79+253x^80+118x^81+52x^82+32x^83+23x^84+12x^85+1x^86+2x^87+7x^88+3x^90+1x^92+1x^94

The gray image is a code over GF(2) with n=576, k=16 and d=256.
This code was found by Heurico 1.16 in 44.9 seconds.