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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+206x^56+200x^57+678x^58+568x^59+1144x^60+796x^61+1290x^62+828x^63+1031x^64+452x^65+444x^66+160x^67+170x^68+52x^69+100x^70+12x^71+33x^72+4x^73+14x^74+6x^76+2x^78+1x^88

The gray image is a code over GF(2) with n=496, k=13 and d=224.
This code was found by Heurico 1.16 in 1.67 seconds.