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

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

Homogenous weight enumerator: w(x)=1x^0+102x^62+238x^64+56x^65+342x^66+260x^67+472x^68+1192x^69+477x^70+2052x^71+435x^72+1288x^73+396x^74+236x^75+240x^76+24x^77+144x^78+12x^79+115x^80+54x^82+32x^84+21x^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 2.23 seconds.