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

generates a code of length 79 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+7x^78+106x^79+7x^80+6x^87+1x^110

The gray image is a code over GF(2) with n=632, k=7 and d=312.
This code was found by Heurico 1.16 in 0.29 seconds.