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

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

Homogenous weight enumerator: w(x)=1x^0+154x^64+202x^65+248x^66+322x^67+340x^68+236x^69+268x^70+68x^71+77x^72+58x^73+52x^74+10x^75+3x^76+8x^78+1x^116

The gray image is a code over GF(2) with n=544, k=11 and d=256.
This code was found by Heurico 1.16 in 0.323 seconds.