The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+242x^54+256x^55+728x^56+888x^57+1328x^58+1684x^59+2177x^60+2124x^61+2044x^62+1668x^63+1247x^64+720x^65+610x^66+252x^67+189x^68+76x^69+86x^70+12x^71+36x^72+10x^74+5x^76+1x^84

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 56.8 seconds.