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  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  1  4  1  1  1  1  1  0  1  1  1  1  4  1  1  4
 0  2 12  6  0  6 12 10  0  6 10 12 14 10  8  4  0  6 12 10  0  6 10 12  0  6 10 12 14  8  2 12  4  6  6 12 14 14  0  0  8  4 10  2 10  8  4  2  0  0  8  8  6 12  6 14 14 12 12  4  4  4 10 10  4  2  2 12
 0  0  8  0  0  0  0  0  8  0  0  0  0  0  8  8  0  0  0  0  0  0  0  8  8  0  0  8  0  8  0  0  8  8  8  0  8  8  8  8  8  0  8  8  8  8  8  8  0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  8  0  8  8  0
 0  0  0  8  0  0  0  8  0  0  0  0  8  8  0  0  0  0  0  0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  0  8  0  8  8  8  8  0  8  0  8  8  8  0  8  8  8  8  8  0  0  0  8  8  8  0  8  8  8  0  0  0  8  0
 0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  8  0  0  8  8  8  0  8  8  0  8  0  0  8  8  0  8  8  0  8  0  0  8  0  0  8  0  0  8  8  8  0  0  8  0  0  8  0  0  0  0  0  8  8  0  0  0  8  8  0  8  8  0
 0  0  0  0  0  8  0  8  0  8  0  0  0  8  0  0  8  0  8  0  8  8  8  8  8  0  0  8  8  8  8  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  8  0  0  0  0  0  8  8  8  0  0  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  8  0  8  8  8  8  8  8  8  0  8  8  0  0  8  8  0  0  8  0  8  0  0  8  8  0  8  0  0  8  0  0  8  8  0  0  8  8  8  0  0  8  0  8  0  8  8  0  8  0  0  8  8  0  0  0  0  0  0  8  8  0

generates a code of length 68 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+830x^64+256x^66+1024x^67+1024x^69+256x^70+640x^72+64x^80+1x^128

The gray image is a code over GF(2) with n=544, k=12 and d=256.
This code was found by Heurico 1.16 in 70.6 seconds.