The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+176x^54+516x^55+1174x^56+1878x^57+3221x^58+5252x^59+7084x^60+8770x^61+9431x^62+8974x^63+7413x^64+4958x^65+2921x^66+1810x^67+979x^68+492x^69+293x^70+70x^71+46x^72+40x^73+19x^74+2x^75+7x^76+6x^77+2x^78+1x^82

The gray image is a code over GF(2) with n=496, k=16 and d=216.
This code was found by Heurico 1.16 in 45.6 seconds.