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

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

Homogenous weight enumerator: w(x)=1x^0+70x^52+110x^53+188x^54+242x^55+371x^56+454x^57+874x^58+1212x^59+1661x^60+2086x^61+1989x^62+2136x^63+1569x^64+1204x^65+846x^66+398x^67+328x^68+206x^69+154x^70+84x^71+83x^72+30x^73+38x^74+22x^75+13x^76+6x^77+5x^78+2x^79+2x^82

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 7.08 seconds.