The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  1  6  1  1 10  1  1 12  1  1  6  1  1  1  1  1  0 12  1 10  1  1  1  1  1  1  1  1  1  0  1 12  1  1  1  1  1  0 12  6 10  1  1  1 12  1  0  1
 0  1  3  6  5  1 12 15  1 10  9  1  1  0  3  5  1  6 15  1 12  9  1 10  5  1  0  6 10 15 12  1  1  3  1 12  3 10 10 12  0  2  4  6  1 15  1  8  9 12  0  5  1  1  1  1  3 10 12  1 15  2  0
 0  0  8  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  0  0  8  0  8  8  0  8  8  8  0  8  0  8  0  0  8  8  0  0  0  8  8  0  0  8  0  8  0  0  8  0  8  0  0
 0  0  0  8  0  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  0  0  0  0  8  8  0  0  8  8  8  8  8  8  0  8  0  0  0  8  0  8  0  8  0  8  0  8  0  0  0  8  8  0  8  0  0  8  0  0  8  8  8
 0  0  0  0  8  0  0  0  8  0  8  0  8  0  0  8  0  0  8  8  0  0  8  0  0  0  0  8  8  8  8  0  8  0  8  0  8  8  0  8  8  8  8  0  0  8  0  0  0  8  8  8  0  0  8  8  8  0  8  0  0  0  8
 0  0  0  0  0  8  0  8  8  0  8  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  0  8  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  0  0  8  8  0  0  0  0  8  8  0  0  0  0  8  0  8  8  0
 0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  8  0  0  0  8  8  8  0  0  0  8  8  8  8  0  8  0  8  8  8  0  0  8  8  0  0  0  0  0  8  8  0  8  0  0  8  0  8  8  8  8  8  8  8  0  8  8  8

generates a code of length 63 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+45x^56+86x^57+291x^58+360x^59+709x^60+874x^61+1133x^62+1188x^63+1157x^64+890x^65+706x^66+368x^67+246x^68+70x^69+37x^70+4x^71+13x^72+2x^74+5x^76+5x^78+1x^86+1x^90

The gray image is a code over GF(2) with n=504, k=13 and d=224.
This code was found by Heurico 1.16 in 0.923 seconds.