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  1  2  1  2  1  1  2  2  1  1  1  1  1  4  2  1  1  1  1  1  1  4  2  1  2  0  1  2  0  1  1  2  2  1
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  8  8  0  0 12  4  0  4  4  0 12  8  8 12 12  0  8  0  4 12  4  4  4  0 12  0  8 12 12  8  4 12  8  4  8  0 12 12  4  4  8 12  8  8  8  8  8  0
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8 12 12 12  0  0  4  8  8  4  0  4  0  8  0  4  4  4  0 12  0  0 12  4 12  4  8 12  8  8 12  0  4  0  4  8 12 12  8  8  8  4  4  4  4  4  0
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  4  0  0  4 12  8  0  4 12  8  8 12  8  0  4 12  0  4  0  4  0 12 12  4  4  4 12  8 12  0 12  4 12  4  0 12  8  8  4  8  8  4  8  8  4  4  0  8
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  8  0  8  8  8  8  0  0  0  8  0  8  0  8  8  0  0  8  8  8  0  8  8  0  0  8  0  8  0  0  0  0  8
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  0  0  8  0  0  0  0  0  0  8  0  8  0  8  8  0  8  0  8  8  8  8  8  8  8  0  0  0  8  0  0  8  0  0  0  8  0  0  8  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  8  0  0  0  8  0  8  0  8  8  8  0  8  8  8  0  8  8  8  0  8  0  8  8  8  0  0  0  8  0  0  0  8  8  0  0  8  8  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+46x^56+76x^57+139x^58+140x^59+204x^60+278x^61+424x^62+878x^63+1257x^64+1416x^65+1260x^66+878x^67+433x^68+210x^69+154x^70+114x^71+75x^72+50x^73+55x^74+30x^75+22x^76+16x^77+14x^78+8x^79+4x^80+2x^81+1x^82+5x^84+1x^88+1x^98

The gray image is a code over GF(2) with n=520, k=13 and d=224.
This code was found by Heurico 1.16 in 1.89 seconds.