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

generates a code of length 88 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+216x^78+436x^79+1014x^80+1228x^81+1854x^82+2544x^83+3462x^84+4536x^85+6364x^86+7272x^87+8110x^88+7064x^89+6350x^90+4692x^91+3473x^92+2316x^93+1720x^94+1012x^95+799x^96+436x^97+272x^98+164x^99+113x^100+36x^101+24x^102+8x^103+19x^104+1x^128

The gray image is a code over GF(2) with n=704, k=16 and d=312.
This code was found by Heurico 1.16 in 99.8 seconds.