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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+238x^80+20x^81+336x^82+68x^83+560x^84+552x^85+560x^86+680x^87+376x^88+196x^89+224x^90+20x^91+207x^92+32x^94+25x^96+1x^156

The gray image is a code over GF(2) with n=688, k=12 and d=320.
This code was found by Heurico 1.16 in 29.3 seconds.