The generator matrix

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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+43x^52+62x^53+140x^54+222x^55+572x^56+744x^57+2214x^58+2596x^59+6409x^60+5834x^61+10045x^62+7724x^63+10206x^64+5874x^65+6463x^66+2574x^67+2031x^68+724x^69+526x^70+156x^71+170x^72+62x^73+49x^74+38x^75+19x^76+12x^77+17x^78+2x^79+3x^80+1x^82+2x^84+1x^90

The gray image is a code over GF(2) with n=504, k=16 and d=208.
This code was found by Heurico 1.16 in 50.2 seconds.