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

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

Homogenous weight enumerator: w(x)=1x^0+130x^56+36x^57+452x^58+252x^59+850x^60+988x^61+2062x^62+2224x^63+3526x^64+3596x^65+4662x^66+3800x^67+3419x^68+2212x^69+1834x^70+912x^71+860x^72+272x^73+340x^74+44x^75+169x^76+84x^78+34x^80+6x^82+2x^84+1x^88

The gray image is a code over GF(2) with n=528, k=15 and d=224.
This code was found by Heurico 1.16 in 22.8 seconds.