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

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

Homogenous weight enumerator: w(x)=1x^0+108x^53+538x^54+1020x^55+1460x^56+2034x^57+3206x^58+4668x^59+6453x^60+8962x^61+8801x^62+8654x^63+6889x^64+4672x^65+2976x^66+2112x^67+1313x^68+788x^69+482x^70+202x^71+108x^72+54x^73+28x^74+6x^77+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 63.9 seconds.