The generator matrix

 1  0  1  1  1  8  1  1 14  1  6  1 14  1  1  1  1  4  1  1  4  1  8  1  1 10  1  1  8  1  1 14  1  2  1  1  4 10  1  1  1 10 12  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  4 10  0  6
 0  1  1  4  3  1  2  9  1  6  1  7  1  6  7  0  9  1 12  1  1  8  1 11 10  1  3 10  1  5  0  1  3  1  5 10  1  1  7 13 15  1  1  5  8 10  2  4  4  8  8  6 14 12  8  8  4  9  6 14 14 14 14  4  8  1  1  1
 0  0  2 10  8 10 10  8 10  0  0  2 12 12 14  4  6 10  6 12 14 10  4  4  4  4  6  6  6  4 14 14  2  0  8  0 12  6 12  6  8 10  0 10  0  2  6  4  8 12  8  6 14  0  6 14 12 12  8  4  2 10 12  2  2 14 12  8

generates a code of length 68 over Z16 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+308x^65+385x^66+348x^67+146x^68+252x^69+309x^70+168x^71+45x^72+60x^73+8x^74+8x^75+4x^79+4x^81+1x^94+1x^98

The gray image is a code over GF(2) with n=544, k=11 and d=260.
This code was found by Heurico 1.16 in 0.25 seconds.