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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+113x^62+4x^63+275x^64+60x^65+382x^66+248x^67+724x^68+764x^69+1064x^70+984x^71+1177x^72+692x^73+734x^74+216x^75+260x^76+84x^77+187x^78+20x^79+96x^80+68x^82+24x^84+12x^86+2x^88+1x^104

The gray image is a code over GF(2) with n=568, k=13 and d=248.
This code was found by Heurico 1.16 in 2.22 seconds.