The generator matrix

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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+144x^55+593x^56+814x^57+1363x^58+2304x^59+2114x^60+2200x^61+1979x^62+2056x^63+1335x^64+628x^65+385x^66+208x^67+128x^68+56x^69+15x^70+24x^71+16x^72+14x^73+1x^74+4x^76+1x^80+1x^82

The gray image is a code over GF(2) with n=488, k=14 and d=220.
This code was found by Heurico 1.16 in 2.95 seconds.