The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+642x^63+1074x^64+1816x^65+1646x^66+2546x^67+2032x^68+1892x^69+1368x^70+1488x^71+767x^72+572x^73+214x^74+212x^75+55x^76+28x^77+4x^78+6x^79+6x^80+12x^81+2x^83+1x^84

The gray image is a code over GF(2) with n=544, k=14 and d=252.
This code was found by Heurico 1.16 in 93.9 seconds.