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  2  2  2  2  1  2  2  2  1  1  1  1  1  4  1  2  1  4  1  1  8  1  1  4  2  2  2  1  1  1  4  0  1  4  0  1  2  1  2  2  1  1  2  4  1  1  4  1
 0 12  0  4  0  0  4 12  0  0 12 12  0  8 12  8 12  0  4 12 12  0  4  8  8  8 12 12  4  0 12  4  8  4  4  0  0 12  0  4  4  8  0 12 12 12  8  0 12  8  4 12  0 12 12  8  4  4  8  8  0 12  8  4  4  0  0  4  4  0 12  8  0  4 12 12 12  0  4  4 12  4 12  8  4
 0  0 12  4  0 12  4  0  0 12 12  8  8 12  4  4  0  8  4  4  0  4  4  8  4  8  0  0  0 12 12  4 12  8 12  8  0  0 12  4 12  0 12  0  0  8  0  4  4  4  4 12 12  8  0  8  8 12  8  0 12 12  4  4  8  4  4 12  8  0  0  4 12 12  0  0  8  0  4  4  8  8  4  4  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  0  0  0  8  0  8  8  8  0  8  0  0  0  8  0  8  8  8  8  8  8  8  0  8  8  8  8  8  8  8  0  0  8  0  8  0  8  8  8  8  0  8  0  0  0  0  0  8  8  8  8  0  8  8  0  0  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  0  8  8  0  8  0  8  8  0  8  0  8  8  8  8  0  8  0  8  0  0  8  8  8  8  0  8  8  0  0  0  8  0  0  8  8  0  8  8  0  0  0  0  0  8  0  0  0  8  0  8  0  0  0  8  8  0  0  0  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  8  8  8  0  0  8  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  8  8  0  0  8  8  8  0  0  8  8  8  8  8  8  0  0  0  8  0  8  8  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  8  8  8  0  0  0  8  8  0  8  8  8  8  0  8  0  0  8  8  8  8  0  8  8  8  0  0  8  8  0  0  8  0  8  8  0  8  0  0  8  0  0  0  8  8  0  8  8  8  8  8  0  0  8  8  8  8  0  8  8  0  8
 0  0  0  0  0  0  0  8  0  0  8  0  8  8  0  0  0  8  8  0  8  0  8  8  0  0  0  8  8  8  0  0  8  0  0  0  8  8  8  0  0  8  8  8  8  0  8  8  0  0  8  0  8  0  0  8  0  8  0  8  8  0  0  8  0  0  8  8  8  8  0  8  8  0  8  0  8  0  8  8  8  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  8  0  8  0  8  8  8  8  8  0  0  8  8  0  8  8  0  0  0  0  0  0  8  8  8  8  0  8  0  0  8  0  8  8  0  0  0  8  0  8  8  8  8  0  8  8  8  0
 0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  8  8  8  8  0  8  8  8  8  0  0  0  8  8  0  8  0  0  8  0  0  0  8  8  8  0  8  0  8  8  8  0  0  0  8  0  0  8  0  8  8  0  8  8  0  0  0  8  0  8  0  0  8  8  0  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+159x^72+244x^74+24x^75+624x^76+164x^77+542x^78+524x^79+961x^80+1744x^81+1888x^82+3680x^83+3823x^84+4344x^85+3746x^86+3304x^87+2020x^88+1808x^89+828x^90+616x^91+691x^92+132x^93+346x^94+44x^95+280x^96+80x^98+101x^100+6x^102+32x^104+9x^108+2x^112+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 42 seconds.