The generator matrix

 1  0  0  1  1  1 10  4  2  0  1  1  1  1 10  1  2  1  1  1  4 14  1  1  8  1  6  1  1  1  8 10  1 12  1  8  1  1  8  1  1  2  1  6  1  1  1  1  1  1  1  6  4 12  1  1  4  1 14  1 14  1
 0  1  0  4  5  1  1  1  1  6  0  8 15 11  6  6  1  7 15 10  1  4 10  9  1 14  1 11 12  2  1  1  8 12 11  1  9  0  1  5  8  6 11  1 12 14 14 15  0 13 11  1  1  1  0  6  1  8  1 11  4  0
 0  0  1  7  3  4  3  2  1  1  6  1  3  2  1  5  2  4  5  0  7  1  6  0  1  7  0 11  3  7 12 13  4  1 15  7 10 10 14  5 11  1  9  0  8  2  3 12 14  8  6  9 12 12  3  6  8 13  5  4  1  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  8  0  8  0  0  8  0  8  8  8  0  8  0  8  0  0  8  8  0  8  8  8  0  0  8  0  8  8  0  0  0  8  8  0  0  8  8  0  0  8  8  0  8  0  0  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  0  8  8  0  8  0  8  8  8  8  0  0  8  8  8  0  0  8  0  0  0  8  0  0  8  0  8  8  0  8  8  8  8  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  8  8  8  0  0  0  0  8  8  8  0  0  0  8  0  0  0  8  8  0  8  0  0  8  8  8  8  0  8  0  0  0  8  8  0  8  0  8  8  8  0  8  0  8  0
 0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  0  0  0  8  8  8  0  0  8  8  0  8  8  8  8  0  8  0  8  0  0  0  0  8  0  8  8  8  0  8  8  0  0  8  0  8  0  8  8  8  0  8  8  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+72x^54+422x^55+995x^56+2160x^57+3321x^58+5524x^59+6276x^60+10188x^61+7962x^62+9954x^63+6409x^64+5660x^65+3020x^66+1924x^67+855x^68+404x^69+201x^70+86x^71+54x^72+20x^73+6x^74+8x^75+1x^76+9x^78+2x^79+1x^80+1x^82

The gray image is a code over GF(2) with n=496, k=16 and d=216.
This code was found by Heurico 1.16 in 36.8 seconds.