The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^54+132x^55+566x^56+816x^57+1259x^58+1972x^59+1976x^60+2832x^61+1981x^62+2092x^63+1136x^64+688x^65+447x^66+156x^67+129x^68+16x^69+25x^70+17x^72+18x^74+11x^76+4x^80

The gray image is a code over GF(2) with n=488, k=14 and d=216.
This code was found by Heurico 1.16 in 4.34 seconds.