The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+92x^53+220x^54+572x^55+797x^56+2282x^57+2706x^58+5882x^59+6426x^60+9372x^61+8563x^62+10106x^63+6357x^64+5734x^65+2561x^66+2174x^67+669x^68+470x^69+259x^70+130x^71+78x^72+24x^73+25x^74+16x^75+5x^76+10x^77+2x^78+3x^80

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 46.6 seconds.