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

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

Homogenous weight enumerator: w(x)=1x^0+112x^56+232x^58+473x^60+128x^61+716x^62+512x^63+1558x^64+768x^65+1576x^66+512x^67+801x^68+128x^69+318x^70+168x^72+86x^74+74x^76+14x^78+9x^80+2x^82+3x^84+1x^92

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 1.96 seconds.