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

generates a code of length 85 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+103x^78+252x^79+394x^80+486x^81+769x^82+778x^83+1004x^84+956x^85+1009x^86+720x^87+584x^88+360x^89+255x^90+168x^91+116x^92+72x^93+58x^94+28x^95+44x^96+10x^97+12x^98+6x^99+4x^101+2x^102+1x^128

The gray image is a code over GF(2) with n=680, k=13 and d=312.
This code was found by Heurico 1.16 in 2.41 seconds.