The generator matrix

 1  0  0  1  1  1  8  1  1  6  1  6  1  2  1  1  1  6  4 10  1  1  6  0  1  8  1  4  2  1  6  1  1  1  1 10 12  1  4 12  1 12  1  8  1 10  6  1  1 12  8 10  2  1  1  1  1  1 14 14  1
 0  1  0  4 13  5  1  8  4  0  7  1  3  1  6  9  2  1  2  1 11  2 10  1  2  1  1  0  1  2  1  5  7  1  6 12 14  4  1  1 15  1 14  1 14  1  1 12 15  1  1  1  1 13  0  3 14  8  0  1  0
 0  0  1  7 15 12  5  2  1  1  4  8  5  1  0  5  9  6  1  3  6  2  1  6 11 15 10  1 10  7 13 15 13  1 13  1  1  9  6  7  7 13  6  4 12  9  8  7  3  9  3  5 11  1 15 10  2 10  1  7  0
 0  0  0  8  8  8  0  8  0  8  0  8  0  8  8  8  8  8  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  0  0  0  8  8  0  8  8  8  8  8  0  0  0  0  0  0  0  8  0  0  0  0  8  0  8  0  0

generates a code of length 61 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+66x^56+516x^57+1058x^58+1140x^59+1097x^60+1092x^61+1008x^62+728x^63+447x^64+448x^65+338x^66+144x^67+61x^68+24x^69+18x^70+4x^71+2x^78

The gray image is a code over GF(2) with n=488, k=13 and d=224.
This code was found by Heurico 1.16 in 0.703 seconds.