The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  8  1  2  2  1  0  1  1  1  2  8  4  1  0  8  1  8  2  1  2  2  2  1
 0 12  0  0  0  0  0  0  0  0  8  4 12 12  8  0 12  4 12  4 12  8 12  0  0  4  4 12  4  8  8 12 12 12  8  8 12  0 12  0  8 12  0 12  4 12  0 12  4  4 12  0  4  8  4  4  8 12 12 12 12  0
 0  0 12  0  0  0  0  0  0  0 12  8  4 12  4  4  4  4  0  8 12 12  8  4  4  8  4  4  0 12 12  4  4  8  8  0 12  8 12  8  8  0  4  0  8 12  4  8 12  8  8 12 12  8  8  0  0 12 12  4 12 12
 0  0  0 12  0  0  8 12 12  4  4 12  8 12 12  0  8 12 12  4  4  4  0  4  0  8  8  8  4  0  4 12  0  0 12  8  4  4  4  0 12  8  8 12 12  0  8  8  4  8  4 12  8  4  0 12  0 12  8  4 12  4
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  8  0 12  4 12  4  8  4  4 12 12 12  4  0  0 12  4  4  0  8  8 12  8 12  0  4  8  4  8  8 12 12  0  8  8 12 12 12  8  4 12  8  0  0  8  8  0  4
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  4  4  0  4  8 12  4  8 12  4  0  8  4  4  4 12  0  0 12 12  0  8  8  4  8  4  8 12 12 12  0  0  8  0  4  0  8  8 12  0  8  8 12  8 12  8  0 12

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

Homogenous weight enumerator: w(x)=1x^0+66x^52+122x^53+168x^54+214x^55+361x^56+440x^57+648x^58+1106x^59+1602x^60+2244x^61+2488x^62+2274x^63+1682x^64+1056x^65+647x^66+392x^67+279x^68+186x^69+124x^70+86x^71+88x^72+40x^73+13x^74+22x^75+17x^76+8x^77+7x^78+2x^79+1x^86

The gray image is a code over GF(2) with n=496, k=14 and d=208.
This code was found by Heurico 1.16 in 6.98 seconds.