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

generates a code of length 77 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+1x^78+22x^79+1x^80+6x^81+1x^82

The gray image is a code over GF(2) with n=616, k=5 and d=312.
This code was found by Heurico 1.16 in 0.279 seconds.