The generator matrix

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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+26x^52+84x^53+276x^54+510x^55+1141x^56+1724x^57+3597x^58+4826x^59+7195x^60+8814x^61+9315x^62+8684x^63+7433x^64+4778x^65+3382x^66+1738x^67+1024x^68+434x^69+291x^70+108x^71+65x^72+34x^73+26x^74+4x^75+11x^76+4x^77+5x^78+2x^79+2x^82+1x^86+1x^90

The gray image is a code over GF(2) with n=496, k=16 and d=208.
This code was found by Heurico 1.16 in 45.8 seconds.