The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+220x^56+428x^57+1045x^58+1400x^59+1980x^60+2132x^61+2407x^62+1980x^63+1814x^64+1268x^65+961x^66+356x^67+178x^68+76x^69+49x^70+36x^71+24x^72+14x^74+4x^75+2x^76+4x^78+5x^80

The gray image is a code over GF(2) with n=496, k=14 and d=224.
This code was found by Heurico 1.16 in 4.33 seconds.