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

generates a code of length 82 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+56x^68+36x^70+12x^71+269x^72+184x^73+260x^74+424x^75+836x^76+1036x^77+1580x^78+2568x^79+3231x^80+3968x^81+3928x^82+3968x^83+3246x^84+2568x^85+1580x^86+1036x^87+736x^88+424x^89+260x^90+184x^91+207x^92+12x^93+36x^94+67x^96+33x^100+15x^104+5x^108+1x^112+1x^116

The gray image is a code over GF(2) with n=656, k=15 and d=272.
This code was found by Heurico 1.16 in 30.6 seconds.