The generator matrix

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

generates a code of length 65 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+42x^56+116x^57+233x^58+318x^59+467x^60+704x^61+1338x^62+1756x^63+2024x^64+2492x^65+2084x^66+1712x^67+1298x^68+674x^69+434x^70+272x^71+172x^72+88x^73+55x^74+26x^75+19x^76+20x^77+10x^78+12x^79+9x^80+3x^82+2x^85+2x^86+1x^98

The gray image is a code over GF(2) with n=520, k=14 and d=224.
This code was found by Heurico 1.16 in 6.1 seconds.