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  2  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  1  1  4  1  1  4  2  2
 0 12  0  0  0  4 12  4  0  0  0  0  4 12  4 12  0  0  0  0  4 12  4  4  0  0  0  0  4  8 12 12 12  4  8  8  8  8  4 12  4  8  8  8  8 12  4 12 12  8  8  8  8 12  4  4 12  8  8 12  4  8  8 12  4  0  8  0  0  4 12  4 12  0 12  8  4  4 12 12 12
 0  0 12  0  4  4 12  0  0  0  4 12  4 12  0  0  8  8 12  4 12  4  8  8  8  8 12  4 12  0  4  8  8  8 12 12  8  8  0 12 12  0  0  4  4  4  4  0  8  0  8 12 12 12 12  8  8  4  4  0  0  0  8  4  4  0  8  4 12  4  4  0  0 12  4 12  4  8  0  4  4
 0  0  0 12  4  0 12  4  8  4 12  8  8  4 12  8  8  4 12  8  8  4 12  8  0 12  4  0  0  4 12  4 12  0  4  8  0 12  8  8  4  8 12 12  0  0 12 12  0  4  8 12  0  0 12  4  8  4  8  4  0  0  4  8  4  0 12  4  0  0  4  4  0  4  8  4  8  8  8  0 12

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

Homogenous weight enumerator: w(x)=1x^0+86x^78+64x^79+249x^80+256x^81+228x^82+64x^83+48x^84+22x^86+5x^88+1x^152

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 28.9 seconds.