The generator matrix

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

generates a code of length 61 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+170x^55+421x^56+1018x^57+1325x^58+2048x^59+2151x^60+2440x^61+2118x^62+1900x^63+1228x^64+880x^65+354x^66+140x^67+48x^68+60x^69+9x^70+26x^71+22x^72+14x^73+4x^75+4x^77+1x^78+1x^82+1x^84

The gray image is a code over GF(2) with n=488, k=14 and d=220.
This code was found by Heurico 1.16 in 4.25 seconds.