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

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

Homogenous weight enumerator: w(x)=1x^0+84x^80+84x^81+197x^82+102x^83+267x^84+336x^85+742x^86+510x^87+737x^88+334x^89+256x^90+82x^91+185x^92+70x^93+75x^94+10x^95+4x^96+6x^97+6x^98+2x^101+3x^102+2x^104+1x^154

The gray image is a code over GF(2) with n=696, k=12 and d=320.
This code was found by Heurico 1.16 in 1.32 seconds.