The generator matrix

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

generates a code of length 66 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+102x^56+264x^57+636x^58+896x^59+1588x^60+2028x^61+3475x^62+4664x^63+7036x^64+7472x^65+9059x^66+7526x^67+7305x^68+4860x^69+3414x^70+1986x^71+1445x^72+648x^73+513x^74+266x^75+175x^76+80x^77+42x^78+22x^79+12x^80+8x^81+12x^82+1x^86

The gray image is a code over GF(2) with n=528, k=16 and d=224.
This code was found by Heurico 1.16 in 77.1 seconds.