The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+46x^53+255x^54+452x^55+1176x^56+1704x^57+3678x^58+4708x^59+7310x^60+8526x^61+10000x^62+8476x^63+7507x^64+4628x^65+3441x^66+1680x^67+1086x^68+346x^69+271x^70+88x^71+58x^72+44x^73+16x^74+20x^75+12x^76+2x^77+2x^78+2x^80+1x^82

The gray image is a code over GF(2) with n=496, k=16 and d=212.
This code was found by Heurico 1.16 in 47.1 seconds.