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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+97x^80+226x^81+483x^82+490x^83+712x^84+768x^85+1105x^86+836x^87+1087x^88+632x^89+583x^90+350x^91+291x^92+122x^93+129x^94+102x^95+79x^96+42x^97+30x^98+12x^99+5x^100+2x^101+5x^102+2x^111+1x^134

The gray image is a code over GF(2) with n=696, k=13 and d=320.
This code was found by Heurico 1.16 in 2.56 seconds.