The generator matrix

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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+66x^61+123x^62+322x^63+386x^64+702x^65+891x^66+1046x^67+1103x^68+1142x^69+808x^70+742x^71+407x^72+258x^73+87x^74+58x^75+17x^76+8x^77+8x^78+8x^79+2x^80+2x^82+3x^84+1x^86+1x^100

The gray image is a code over GF(2) with n=544, k=13 and d=244.
This code was found by Heurico 1.16 in 2.63 seconds.