The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+170x^55+584x^56+936x^57+1848x^58+2762x^59+3299x^60+4782x^61+4221x^62+4792x^63+3458x^64+2588x^65+1578x^66+840x^67+422x^68+216x^69+153x^70+38x^71+38x^72+20x^73+8x^74+6x^75+4x^76+2x^77+1x^80+1x^84

The gray image is a code over GF(2) with n=496, k=15 and d=220.
This code was found by Heurico 1.16 in 12.1 seconds.