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  2  2  2  2  4  1  0 12  1  1  1  1  8  1  1 12  1  8  1  1  2  8  2  1  2  1  1  2  1  1  1  2  2  2  1  1  1  1  0  2  1  2  2  2
 0  2  0  2  0  0  2 10  8  0  6  6  4  2  2 12  0 12  6 14 10 12 14 12 14 14  8  4 12 14  2  2  2  2 12  4  2  0 14  8  8  4  2 10  2  0 14 14  2  6 10  8 14  0 12  6  8  4 10  8  8 14  6  2 10  2  2  2  6 12 12
 0  0  2  2  0  6 10  8  6  4  6 12 12 12 14  2  4 14  8 10  4 10 14  0  0 12  2  2  6  0  2  2  6  8  2 10 10  6 10  2  8  4 10 14  0  2  4  4  0  6  6 10  6  8 10 10  6  6 14  6  2 14  2  0  6  8  8  2  2  8 10
 0  0  0  4  0  0  4  0  0  0 12  0  0  0  4  8  0  8  8  4  8  0  4  0  8  8  0  8  8  4 12 12 12  4  0  4  0  4  8 12  4 12  8  0 12 12 12  0 12 12  8 12  0  4 12  8 12 12  8  4  8  0 12 12  4  8 12  8 12 12  4
 0  0  0  0 12  0 12  4  4  4 12  4  8  0  8 12  8 12  0  8  4  8  0  0  4  0  4  0  8  8 12  4 12  4  4  4 12  8  8  0  4  4  4  0  8  4 12  8  0  4  4  8 12 12 12 12  8 12  8  8  8  8  0  0  0  8  4  4  0  8  4
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  8  8  8  0  0  8  0  0  8  0  8  8  0  8  0  8  8  0  0  0  0  0  0  8  0  8  0  8  0  0  8  8  0  8  8  8  8  0  8  8  8  0  0  0  8  0  0  0  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+158x^62+228x^63+676x^64+740x^65+1158x^66+1748x^67+2459x^68+3232x^69+3806x^70+4420x^71+3898x^72+3456x^73+2294x^74+1600x^75+1134x^76+708x^77+440x^78+192x^79+234x^80+52x^81+68x^82+4x^83+39x^84+4x^85+12x^86+6x^88+1x^96

The gray image is a code over GF(2) with n=568, k=15 and d=248.
This code was found by Heurico 1.16 in 22.6 seconds.