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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  4  1  2  2  2  2  2  0  2  1  2  1  1  1  1  4  2  0  2  2  1  1  1  4  8  1  4  1  1  1  1  2  1  2  1  1  1  1  1
 0 12  0  0  0  4 12  4  0  8  0 12  0  0 12 12  4  0  8  8  4  4  0  4  4  8  4  8 12  4  8  8  4 12 12 12 12  4 12 12  8 12  4 12  0 12 12  8 12  4  8  4 12  0  8 12  8  0  8 12  0  8  4  0  0  0  4  4 12  4  4  4  0  8 12 12  0 12  4  8 12  0  8  4  0
 0  0 12  0  4  4 12  0  0  0 12  8  0 12  4  0 12  8 12 12 12  4 12 12  0  0  8  4  8  4 12 12  8  0 12 12  0  0  0  4  0 12  4  8  8  0  8  0  8  8  4 12  4  4  0  8  0  4  0  4 12  8  8  4  4 12  0  4 12  8  8  8  0  4  0  0  8  8 12 12 12  8  4 12  0
 0  0  0 12  4  0 12  4  0  4 12 12  8  8  4  8  0  4  4  0  8  4  4  0  0  8  4  8  4  4  8  4  8  4  8 12  4  8  8  0  4  4  0  0  4  0  8  0  8  4  0  0  4  0  4  0  4  0  0  8  0 12  8  0  0  4 12  8  4 12  4 12 12  8  4  0 12 12  0 12  0  0  8  4  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  0  0  8  8  8  0  8  0  8  8  0  0  0  8  8  8  0  0  0  8  8  0  8  0  8  0  8  0  0  0  8  8  8  8  8  8  8  8  0  0  8  0  0  8  0  8  8  8  8  0  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  8  0  0  0  0  8  8  0  0  8  0  8  8  0  8  8  8  8  0  0  0  8  8  8  0  8  8  8  0  8  0  8  8  0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  0  0  0  8  8  8  0  8  0  8  0  8  0  0  8  8  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  0  0  0  0  8  8  0  8  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  0  0  8  0  8  8  8  8  8  0  8  0  8  8  0  0  0  0  8  8  0  8  8  8  8  0  8  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8
 0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  8  8  8  8  8  0  0  8  8  0  0  8  0  8  8  8  8  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  8  0  0  8  8  0  0  0  0  0  8  8  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  0  8  8  0  8  8  8  8  8  0  8  0  0  8  0  8  0  0  8  0  8  0  8  0  8  8  8  0  0  8  0  0  0  0  8  8  0  0  8  8  8  8  0  0  8  0  8  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+42x^72+118x^73+152x^74+218x^75+303x^76+466x^77+413x^78+604x^79+764x^80+1292x^81+1934x^82+3284x^83+4617x^84+4500x^85+4663x^86+3204x^87+1877x^88+1386x^89+749x^90+598x^91+406x^92+310x^93+192x^94+216x^95+134x^96+100x^97+72x^98+60x^99+31x^100+20x^101+11x^102+8x^103+13x^104+5x^106+2x^108+1x^110+1x^112+1x^124

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 40.8 seconds.