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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+114x^78+92x^79+290x^80+220x^81+511x^82+584x^83+904x^84+924x^85+1113x^86+856x^87+843x^88+580x^89+447x^90+248x^91+211x^92+68x^93+82x^94+12x^95+34x^96+22x^98+17x^100+14x^102+3x^104+1x^110+1x^136

The gray image is a code over GF(2) with n=688, k=13 and d=312.
This code was found by Heurico 1.16 in 2.7 seconds.