The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  1  1  1  1  1  1  1  8  4  4  2  1  8  1 12  2  1  0  4  1  1  1  2  1  1  1  1  2 12  1 12  1  2  1
 0  2  0  2  0  0 14  6  4  2  4 14 12  6 12  2  0 12  0  8 12 12  0  8 12  4 12 12 14 14  2 10  6 10  2  2  4  2 12  2  2  2  2  6  4  2  2  2 14  6 14 12  0 10  0 10  2  8 12 12 10  2
 0  0  2  2 12  6 14  0  4  6  2 12  0 10  6 12  8  2  2  0  8 14 14 12  4  2  2  6  0 12  2  0  6 12 14  4  2 10  6 10 14  0  2 10  6 14 12  4 12  4  2  2 14 14  4  8  8 12  2  8  0  2
 0  0  0  4  0  0 12  8  8 12  0  0  8  4  0  8  0  4  4  4 12  4  4  4 12  0  0  8 12  4  0  4  8 12  8  0  8  0  8 12 12  0  4 12  0  8  8  4 12  0  8 12  4 12  0 12  8  0  4  0  0  0
 0  0  0  0  8  0  0  0  8  0  0  0  8  0  0  0  8  0  0  8  8  0  0  8  8  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  8  8  0  8  8  0  0  0  0  8  8  8  0  8  0  0  8  0  0  8  0  0
 0  0  0  0  0  8  0  8  8  8  8  0  0  8  0  8  8  0  8  0  8  0  8  0  8  0  8  0  0  0  8  8  0  8  8  0  8  0  0  0  8  0  8  8  8  8  0  8  8  8  8  8  0  0  0  8  8  8  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  0  8  0  8  8  0  8  0  0  8  0  8  0  8  8  0  8  8  8  0  0  8  8  0  0  0  0  0  8  8  0  8  0  8  0  0  0  8  0  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+50x^53+199x^54+452x^55+683x^56+944x^57+1637x^58+2446x^59+3463x^60+4330x^61+4553x^62+4444x^63+3386x^64+2260x^65+1586x^66+928x^67+595x^68+386x^69+194x^70+96x^71+58x^72+28x^73+19x^74+18x^75+2x^76+2x^77+2x^78+4x^80+1x^82+1x^90

The gray image is a code over GF(2) with n=496, k=15 and d=212.
This code was found by Heurico 1.16 in 18.6 seconds.