The generator matrix

 1  0  1  1  6  1  1  1 12  1  8  1  2  1  1  1  4  1  1 10  1  1  0  1  6  1  1  1  1 12 14  1  1  1  2  1 12  1  4  1 14  1  1  0  1  1  1  1  1  1 14  1  0  0  1  1  1  1  6  1  1  1 14  1  1  1  8 12  1  4  0  4
 0  1  1  6  1  7  3  4  1  2  1  5  1  8 14 15  1  3  0  1 13 14  1  9  1  3 12  4  5  1  1  3 10  6  1 11  1  1  1 15  1 10  1  1  8 13  9  2 12  7  1 14  0  2 12 11 14  1  1  0  4  9  1  4  1 13  1  1 10  4  1  1
 0  0  2  0  0  2  0  2  6 10 12  8  2  4  4  6  2 12  6  0  4 10  6  6 14  6 14  4 14  8 14  0  6  6  4 10 14  4  4  8  4  0 10  6 10  2  8 12  0 12 12  4  2 10 10 10  0  8  6  6  4  4 12  2  6  4 10  8  8  2 12 10
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  8  0  8  8  0  8  8  0  0  0  8  8  8  8  8  0  0  8  8  8  8  8  8  8  0  0  8  0  0  8  8  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  0
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  0  0  0  0  0  0  0  8  8  0  8  0  0  0  0  8  8  0  8  8  8  0  0  8  0  8  0  0  8  0  0  8  8  8  8  0  8  8  8  8  0  8  8  0  0  0  8  0  8  8  8  0  0  8  0  8  8
 0  0  0  0  0  8  0  8  8  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  8  0  8  0  8  0  8  8  0  0  8  8  8  0  8  0  8  0  0  8  0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  8
 0  0  0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  0  8  0  0  8  0  0  8  8  0  8  8  0  8  0  8  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  0  8  0  8  0  0  0  8  0  8  0  8  8  0  8  8  8  0  8  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+100x^64+288x^65+695x^66+920x^67+2285x^68+2252x^69+3960x^70+3248x^71+5468x^72+3304x^73+3982x^74+2064x^75+2227x^76+880x^77+526x^78+272x^79+119x^80+56x^81+41x^82+24x^83+29x^84+4x^85+10x^86+8x^88+2x^90+3x^92

The gray image is a code over GF(2) with n=576, k=15 and d=256.
This code was found by Heurico 1.16 in 15.1 seconds.