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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+292x^63+112x^64+460x^65+294x^66+580x^67+746x^68+588x^69+276x^70+364x^71+82x^72+156x^73+6x^74+68x^75+18x^76+44x^77+8x^79+1x^112

The gray image is a code over GF(2) with n=544, k=12 and d=252.
This code was found by Heurico 1.16 in 80.1 seconds.