The generator matrix

 1  0  1  1  1  6  1  4  1  1  2  1  1  2  1  1  1  2  4  1  1  4  1  1  1  1 14  1  1  1 14  1  1  1  0  1  0  1  4 10  1  1  1  1  1  2  6  1  1  6  1  2 14  0  1  2 12  2  0  1  2
 0  1  1  6  7  1  3  1  4  5  1 10  8  1  9  6  7  1  1  2  3  1 12  9 10 15  1 11  6  4  1  1  8  1  1 13  1  6  1  1  2  7 13  4  0  1  1  9 12  1  1 14  1  1  1 14  1 12  8  2  2
 0  0  2  0 14  0  0  6  2  8 14  2  0  8 10  4  4 10 10 14 14  8  6  4  0  0 12 14 10  4 14 14 14 12  2 12  8  4  6  4 10  0 14  8 10  0  6 14 12 10  8 10 14 10  4  2  6  2  2  2  2
 0  0  0 12  0  0  8 12  0  8 12  4 12 12  4 12 12  8  0 12  8  4  8 12  8  0  0 12  4  0 12  4 12  8  4  4  0  0  4  4  0 12  4  4  8  4  0  0 12  0 12  8 12 12  0 12  0  8  8  0  8
 0  0  0  0  8  0  0  8  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  0  8  8  8  0  8  8  8  0  0  8  8  8  0  8  8  8  8  8  0  8  8  0  0  8  8  0  8  8  0
 0  0  0  0  0  8  8  0  8  0  0  8  8  8  0  8  8  0  8  0  8  8  8  0  0  0  0  8  8  8  8  8  0  8  0  0  8  0  8  0  0  8  0  0  8  0  0  8  8  8  0  0  0  0  8  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+290x^54+376x^55+1181x^56+1700x^57+2897x^58+3332x^59+4267x^60+4508x^61+4767x^62+3568x^63+2568x^64+1440x^65+1031x^66+340x^67+257x^68+92x^69+89x^70+38x^72+4x^73+12x^74+8x^76+2x^78

The gray image is a code over GF(2) with n=488, k=15 and d=216.
This code was found by Heurico 1.16 in 25.7 seconds.