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  1  1  1  1  2  2  1  1  1  1  2  2  2  2  1  1  4  2  2  0  4  8  1  1  2  2  2  2  4  1  1  4  4  0  8  2  2  1  1  4  4  8  0  2  2  2  2  4  2  2  1  1
 0 12  8  4  0 12  8  4  0 12  8  4  0 12  8  4  0 12  8  4  0 12  8  4 12  4  0 12  8  4 12  4  0  8 12  4  0  8 12  4  0  8 12  0  8  4  4  4 12  4 12  4  0  8  8  0  8 12  4  4  4  0  8 12  4  0  8  8  8 12  4  0  8  0 12  0 12  0

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

Homogenous weight enumerator: w(x)=1x^0+34x^78+4x^79+16x^80+4x^81+2x^82+1x^84+2x^86

The gray image is a code over GF(2) with n=624, k=6 and d=312.
This code was found by Heurico 1.16 in 0.327 seconds.