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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+98x^51+165x^52+246x^53+311x^54+328x^55+462x^56+664x^57+1124x^58+2204x^59+3540x^60+4632x^61+5238x^62+4700x^63+3467x^64+2218x^65+1205x^66+654x^67+416x^68+318x^69+251x^70+172x^71+126x^72+108x^73+54x^74+36x^75+14x^76+4x^77+8x^78+2x^81+1x^82+1x^100

The gray image is a code over GF(2) with n=496, k=15 and d=204.
This code was found by Heurico 1.16 in 26.2 seconds.