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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+24x^78+7x^80

The gray image is a code over GF(2) with n=608, k=5 and d=312.
This code was found by Heurico 1.16 in 0.272 seconds.