The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+174x^64+124x^65+602x^66+856x^67+1677x^68+1540x^69+2480x^70+1616x^71+2465x^72+1540x^73+1598x^74+856x^75+525x^76+124x^77+114x^78+34x^80+18x^82+11x^84+18x^86+6x^88+2x^90+2x^92+1x^100

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 4.35 seconds.