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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+104x^79+349x^80+412x^81+770x^82+970x^83+1366x^84+1528x^85+2042x^86+1968x^87+1890x^88+1358x^89+1273x^90+736x^91+529x^92+300x^93+242x^94+188x^95+138x^96+82x^97+83x^98+14x^99+14x^100+16x^101+6x^102+4x^103+1x^132

The gray image is a code over GF(2) with n=696, k=14 and d=316.
This code was found by Heurico 1.16 in 7.38 seconds.