The generator matrix

 1  0  1  1  1  6  1  1 12  1 10  1  1  8  1  1 14  1  1  4  1  1  2  1  1 12  1 14  1  1  1  1 14  0  1  1  1  1  2  1  1  1  1 12  1  1  4  1  1  1  1  1  1  2  1  8  1  1  1 12  2  8 14  1  1  1  1  1  1  0  8
 0  1 11  6 13  1 12  3  1 10  1  5 15  1  8  1  1 14  4  1  7  2  1  9 15  1  8  1 13 14  4  2  1  1 11 10  8 12  1  1  8  3  5  1  1  7  1  9  0  6  6  7  2  1  4  1  7 13  2  1  1  1  1 10 11  7  1  3  1  1  1
 0  0 12  0  4  0  0  8  0  8  0  0  8 12 12  4 12 12 12  4  4 12 12  8  8  8  4 12  4  4  4  4 12  8  4  0  4  0 12 12  4  0  0  0 12 12  4  8  8  8  0 12 12 12  0 12 12 12  4  0  8  4  4  4 12  8  8  0  4  8 12
 0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  8  0  8  0  0  0  8  8  0  0  0  0  0  8  0  8  8  8  8  0  8  0  0  8  0  8  8  0  0  8  8  0  8  8  0  0  8  0  0  8  0  0  0  0  8  8  8  0  8  8  0  0  8  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  8  0  8  8  8  8  0  8  8  8  8  8  8  8  8  8  0  0  8  8  0  8  0  8  8  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0  0  8  0  0  8  0  0  8  8  0  8  0  8  0  8  0  8  8  8  0  8  8  0  0  0  0  8  8  8  8  0  8  0  0  8  8  8  8  0  0  8
 0  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  0  0  8  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  0  8  0  8  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  0  0  8  8  0  8  0

generates a code of length 71 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+175x^64+180x^65+576x^66+840x^67+1511x^68+1740x^69+2142x^70+2160x^71+2158x^72+1740x^73+1426x^74+840x^75+521x^76+180x^77+124x^78+16x^80+12x^82+19x^84+6x^86+8x^88+2x^90+5x^92+2x^96

The gray image is a code over GF(2) with n=568, k=14 and d=256.
This code was found by Heurico 1.16 in 6.6 seconds.