The generator matrix

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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+88x^52+32x^53+349x^54+324x^55+1082x^56+1264x^57+3441x^58+2736x^59+5238x^60+3568x^61+5698x^62+2776x^63+2977x^64+1232x^65+1147x^66+304x^67+280x^68+48x^69+90x^70+4x^71+50x^72+19x^74+10x^76+6x^78+2x^80+1x^82+1x^86

The gray image is a code over GF(2) with n=488, k=15 and d=208.
This code was found by Heurico 1.16 in 13 seconds.