The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+318x^57+382x^58+848x^59+1046x^60+1096x^61+1039x^62+1026x^63+1015x^64+730x^65+295x^66+224x^67+39x^68+64x^69+10x^70+30x^71+10x^72+16x^73+1x^76+1x^82+1x^86

The gray image is a code over GF(2) with n=496, k=13 and d=228.
This code was found by Heurico 1.16 in 41.9 seconds.