The generator matrix

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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+108x^67+293x^68+268x^69+257x^70+318x^71+202x^72+202x^73+206x^74+116x^75+53x^76+8x^77+9x^78+2x^79+1x^88+2x^89+2x^92

The gray image is a code over GF(2) with n=568, k=11 and d=268.
This code was found by Heurico 1.16 in 0.378 seconds.