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  2  2  1  1  1  2  1  1  1  1  1  1  2  1  2  1  4  1  1  1  2  1  4  1  1  1  1  1  1  2  1  1  1  1  1  2
 0 12  0  4  0  0  4 12  0  8  4  4  0  4  4  8  0  0  0  8  8 12  0 12  4 12 12  4 12  4 12 12 12 12  4  4  0  8  4  4 12  0  4 12  8  0  4  0 12  8  0  4  8  4 12 12  0 12 12  0  8 12
 0  0 12  4  0 12  4  0  8  4  0  4  0 12  0  4  8  8  0  8  4  0  4  8  4 12  0  4  0  0  8  8  0 12 12 12  8  0 12  8  8 12  4 12  0  8 12  4  8 12  0 12 12  4 12  4 12  8  4 12  8  0
 0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  0  8  0  8  0  0  8  8  0  0  8  0  0  8  8  0  8  0  0  0  8  8  0  0  8  0  8  8  0  0  0  8  8  8  0  8  8  0  0  0  8  0  8  8  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  8  0  8  0  0  8  8  8  8  0  0  8  0  8  8  8  8  0  0  8  0  0  0  0  8  8
 0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  8  0  8  8  0  0  8  8  0  8  0  0  0  0  8  8  8  8  0  0  0  0  0  0  0  0  8  8  8  0  0  0  8  0  0  8  0  8  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  8  8  0  0  0  8  0  8  0  8  0  0  8  0  8  8  0  8  8  8  0  8  8  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  8  8  0  8  0  0  8  8  8  8  8  8  0
 0  0  0  0  0  0  0  8  0  0  8  8  0  0  0  8  8  8  8  0  0  8  8  8  8  0  0  0  8  0  8  8  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  0  8  8  8  0  0  8  0  0  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+60x^53+98x^54+108x^55+87x^56+152x^57+250x^58+284x^59+544x^60+1464x^61+2134x^62+1482x^63+592x^64+254x^65+236x^66+114x^67+32x^68+82x^69+86x^70+50x^71+20x^72+34x^73+10x^74+10x^75+2x^77+2x^78+3x^80+1x^104

The gray image is a code over GF(2) with n=496, k=13 and d=212.
This code was found by Heurico 1.16 in 43.6 seconds.