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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+54x^52+124x^53+240x^54+410x^55+528x^56+1108x^57+1452x^58+2624x^59+3577x^60+3956x^61+4788x^62+3950x^63+3548x^64+2614x^65+1325x^66+1088x^67+552x^68+338x^69+194x^70+102x^71+83x^72+46x^73+26x^74+16x^75+8x^76+6x^77+6x^78+2x^79+1x^82+1x^84

The gray image is a code over GF(2) with n=496, k=15 and d=208.
This code was found by Heurico 1.16 in 21 seconds.