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  1  1  2  2 12  8  2  2  1  1  1  0  2  2  2  1  1  1  1  1  2  2  1  2  2 12  2 12  1  1  8  1  1  1  2  1  8
 0  2  0  0  0  2  6 14  4  4 10 10 10  2  0  4  6  4  6  6  8 12  6 12 14 14  4  2  6  0 12  4  6  2  4  0  2  2  4 14  8  0 12  6 14  6  4 10  4  6  2 10 12 14  8  2 14 10 14 14 14  2
 0  0  2  0  2  2  2  0  8 10  0  2  4  2  6 12  8  6 14  0 12 10  6  4  4  6  2  6 10  2  2  0  4  8  6 12  2 12 10  8 10  6  8  2  6 12  6 10 14  6  2 12 12 10  4  2  4 12  4 12  2  4
 0  0  0  2  2  0  2  2  2 14  4 10  2 12  0  8  8 10  6 14  4  4  4 10 12  0 10 10  4  6  0  2  4 14 12  4 12 14  4  4  6 10  6  6  8 10  2  8 14  6  2 10  2  6  8  6  4  2  6 14 12 14
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  0  8  0  0  0  8  0  8  8  8  8  0  0  8  8  0  0  0  8  8  8  0  0  0  0  8  8  0  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  8  0  8  8  0  0  0  8  8  8  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  8  0  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  0  8  8  8  0
 0  0  0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  8  0  8  0  0  0  8  0  8  0  8  0  0  0  0  8  8  8  0  0  8  0  8  0  8  8  0  8  0  0  8  8  0  0  8  0  0  8  8  8  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+242x^53+452x^54+944x^55+1321x^56+2282x^57+3020x^58+5494x^59+5313x^60+10050x^61+7333x^62+9964x^63+5636x^64+5472x^65+2926x^66+2288x^67+1137x^68+826x^69+377x^70+244x^71+85x^72+70x^73+30x^74+10x^75+5x^76+2x^77+5x^78+5x^80+1x^84+1x^86

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 66.6 seconds.