The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+306x^55+964x^56+2364x^57+3117x^58+5598x^59+6740x^60+9544x^61+8403x^62+9788x^63+6716x^64+5412x^65+3127x^66+2026x^67+669x^68+418x^69+173x^70+102x^71+27x^72+20x^73+12x^74+4x^75+3x^76+2x^77

The gray image is a code over GF(2) with n=496, k=16 and d=220.
This code was found by Heurico 1.16 in 37.2 seconds.