The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^56+146x^57+241x^58+296x^59+516x^60+350x^61+984x^62+380x^63+496x^64+210x^65+155x^66+104x^67+69x^68+28x^69+26x^70+4x^71+11x^72+16x^73+2x^74+2x^77+1x^100

The gray image is a code over GF(2) with n=496, k=12 and d=224.
This code was found by Heurico 1.16 in 0.558 seconds.