The generator matrix

 1  0  1  1  1  8  1  1 14  1  1  2  2  1  1  1  1  4  1  1  4  1  1 14  1  1  8  1 10  1  1  8  1  1  2  1  1  1  4  6  1  1 12  1 14  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  2  1  1  1  1  1  4  1  1  1  4  0 10  8  0  1
 0  1  1  4  3  1  2  7  1  6  9  1  1  0  9  6  7  1 12  1  1  4 13  1  5 10  1 11  1 12  5  1  0 13  1  8  3  7  1  1 10  2  1 15  1  3 10  6 14  6 10 14 10 10  8 14  4  0  4  4  8 14  0  4 12  4 12  5  1  1  2  1  9  0  2  1  2  1  1  1  7
 0  0  2 10  8 10 10  2 12  0  8  0  2  4  6 12 14 10  6 12 14 12 14  0  8  6 12 12  6  0  4  6 14  2  4 10  6 12 12  6 14 12  8  0 10  2 10  8 12  6  4 14  0  8 14 10  2 10  0  8  6  2 10  4 12 12 10  2  8 14  0  2  0 12  6  4  8 14  0  2  6

generates a code of length 81 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+357x^78+264x^79+404x^80+214x^81+293x^82+196x^83+157x^84+54x^85+80x^86+8x^87+6x^88+4x^90+4x^94+4x^98+2x^114

The gray image is a code over GF(2) with n=648, k=11 and d=312.
This code was found by Heurico 1.16 in 4.27 seconds.