The generator matrix

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

generates a code of length 85 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+67x^72+14x^73+88x^74+84x^75+213x^76+320x^77+488x^78+708x^79+1230x^80+1346x^81+3050x^82+2280x^83+5159x^84+2784x^85+5157x^86+2280x^87+3010x^88+1346x^89+1207x^90+708x^91+442x^92+320x^93+166x^94+84x^95+79x^96+14x^97+42x^98+23x^100+25x^102+12x^104+11x^106+3x^108+4x^110+2x^114+1x^120

The gray image is a code over GF(2) with n=680, k=15 and d=288.
This code was found by Heurico 1.16 in 32.7 seconds.