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

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

Homogenous weight enumerator: w(x)=1x^0+30x^78+272x^79+78x^80+314x^81+79x^82+164x^83+31x^84+42x^85+2x^86+8x^87+2x^88+1x^134

The gray image is a code over GF(2) with n=648, k=10 and d=312.
This code was found by Heurico 1.16 in 0.4 seconds.