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

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

Homogenous weight enumerator: w(x)=1x^0+46x^56+292x^57+561x^58+1030x^59+1595x^60+2400x^61+3324x^62+5148x^63+6393x^64+8026x^65+7951x^66+7912x^67+6477x^68+5482x^69+3290x^70+2274x^71+1439x^72+874x^73+467x^74+248x^75+136x^76+78x^77+46x^78+26x^79+9x^80+9x^82+2x^83

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 71.5 seconds.