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

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

Homogenous weight enumerator: w(x)=1x^0+28x^77+82x^78+6x^80+4x^82+4x^85+2x^94+1x^96

The gray image is a code over GF(2) with n=624, k=7 and d=308.
This code was found by Heurico 1.16 in 0.3 seconds.