The generator matrix

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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+50x^53+109x^54+294x^55+590x^56+906x^57+1677x^58+3042x^59+4848x^60+7332x^61+9250x^62+9644x^63+9016x^64+7144x^65+5013x^66+3172x^67+1624x^68+866x^69+425x^70+194x^71+129x^72+70x^73+57x^74+34x^75+15x^76+16x^77+12x^78+4x^79+1x^82+1x^84

The gray image is a code over GF(2) with n=504, k=16 and d=212.
This code was found by Heurico 1.16 in 51.6 seconds.