The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  8  2  1  1  1  1  1  4  1  1  1  1  1  1  0  1  8 12  1  1  2  2  1  2  1  8  2  1  8  1  2 12  1  2 12  1 12  2
 0  2  0  6  4 14 12  2  0  6 12 10  8 14 12  2  0 14  8 14  6 12 10  2 14  2  0  2  4 14  2 14 10  2  0 12  8  2  2  2  2 12 12 10  6  0 14 12  2  6  8  4 14  2  2 14  6  2 12  2 14
 0  0 12  0  4  4  0  4  0  8  0  8 12 12 12  4  8  8  4 12  8  0  0  4 12 12  4 12 12 12  4  0  8  0  0  0  8  8  4 12  0  4  8  8  0  0  4  8 12  0  4 12  4 12  0 12  8  8  4  0  4
 0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  8  8  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  0  8  0  0  0  8  8  8  0  8  0  8  8  0  0  0  0  0  8  0  0  0  0  0  0
 0  0  0  0  8  0  0  8  8  8  8  0  8  0  0  8  0  8  8  8  8  8  8  8  0  8  0  0  0  0  8  8  8  8  0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  0  8  0  0  8  0  8  0  0  8  0
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  8  0  0  0  8  8  8  8  8  0  0  8  0  8  0  8  8  8  0  8  0  8  0  0  0  8  8  0  8  8  8  0  0  8  0  8  8  8  0  8  0  0  0  8  8  8
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  8  8  0  0  0  0  0  0  8  0  0  8  0  8  0  0  8  0  0  0  0  0  8  0  0

generates a code of length 61 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+116x^54+104x^55+381x^56+472x^57+652x^58+824x^59+947x^60+1272x^61+962x^62+952x^63+560x^64+296x^65+328x^66+168x^67+61x^68+8x^69+40x^70+25x^72+12x^74+7x^76+2x^78+1x^80+1x^84

The gray image is a code over GF(2) with n=488, k=13 and d=216.
This code was found by Heurico 1.16 in 1.57 seconds.