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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+25x^80+4x^82+2x^84

The gray image is a code over GF(2) with n=624, k=5 and d=320.
This code was found by Heurico 1.16 in 0.341 seconds.