The generator matrix

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

generates a code of length 58 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+465x^54+880x^55+1358x^56+1304x^57+1192x^58+848x^59+646x^60+512x^61+454x^62+256x^63+196x^64+40x^65+32x^66+5x^68+1x^70+1x^72+1x^76

The gray image is a code over GF(2) with n=464, k=13 and d=216.
This code was found by Heurico 1.16 in 1.44 seconds.