The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+77x^56+282x^57+443x^58+730x^59+946x^60+1068x^61+1219x^62+1038x^63+923x^64+730x^65+358x^66+178x^67+94x^68+58x^69+20x^70+2x^71+7x^72+4x^73+6x^74+4x^75+2x^77+1x^78+1x^90

The gray image is a code over GF(2) with n=496, k=13 and d=224.
This code was found by Heurico 1.16 in 1.03 seconds.