The generator matrix

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

generates a code of length 58 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+224x^52+416x^53+1043x^54+1284x^55+2208x^56+1592x^57+2925x^58+1904x^59+2155x^60+996x^61+840x^62+372x^63+239x^64+48x^65+47x^66+24x^67+33x^68+20x^69+8x^70+3x^72+1x^78+1x^80

The gray image is a code over GF(2) with n=464, k=14 and d=208.
This code was found by Heurico 1.16 in 3 seconds.