The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+29x^54+94x^55+122x^56+310x^57+476x^58+592x^59+852x^60+1054x^61+1214x^62+1090x^63+816x^64+616x^65+399x^66+228x^67+115x^68+64x^69+46x^70+30x^71+7x^72+2x^73+9x^74+12x^75+5x^76+2x^77+2x^78+2x^79+2x^80+1x^94

The gray image is a code over GF(2) with n=496, k=13 and d=216.
This code was found by Heurico 1.16 in 1.49 seconds.