The generator matrix

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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+32x^68+300x^69+60x^70+240x^71+31x^72+348x^73+2x^74+8x^75+1x^98+1x^106

The gray image is a code over GF(2) with n=568, k=10 and d=272.
This code was found by Heurico 1.16 in 0.187 seconds.