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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+64x^72+4x^73+50x^74+44x^75+280x^76+164x^77+288x^78+420x^79+945x^80+788x^81+2262x^82+1180x^83+5182x^84+1496x^85+6586x^86+1496x^87+5115x^88+1180x^89+2238x^90+788x^91+866x^92+420x^93+308x^94+164x^95+219x^96+44x^97+42x^98+4x^99+66x^100+2x^102+32x^104+22x^108+7x^112+1x^120

The gray image is a code over GF(2) with n=688, k=15 and d=288.
This code was found by Heurico 1.16 in 32.7 seconds.