The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+69x^54+340x^55+864x^56+2370x^57+3259x^58+5506x^59+6438x^60+9618x^61+8317x^62+9776x^63+6843x^64+5946x^65+2962x^66+1808x^67+764x^68+342x^69+131x^70+100x^71+28x^72+20x^73+11x^74+6x^75+6x^76+8x^77+3x^78

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 37 seconds.