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  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2
 0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0 12  0  4  8  4  8  4  8  4  8  4  8  4  8  4  8  4  8  4  8  4  8  4  8  4  8  4  8 12  8  4  8  4  8  4  0 12  0 12 12 12  0
 0  0  8  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  8  0  8  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  0  8  0  0  0  0  0  0  0  0  0  8  8
 0  0  0  8  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  0  8  8  0  8  0  8  0  0  8  0  8  0  0  0  0  0  0  8  8  0
 0  0  0  0  8  0  8  0  0  8  8  8  8  8  0  8  8  0  8  0  0  8  0  8  0  8  0  8  8  0  8  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  8  0  8  8  0  8  8  0  0  0  8  0  0  8  0  8  0  0  0  8  8  0  0
 0  0  0  0  0  8  0  8  8  8  8  0  8  0  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  0  0  0  8  8  0  0  8  8  8  8  8  8  8  0  8  0  0  8  0  0  0  8  0  0  0  0  0  8  8  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+45x^68+32x^69+72x^70+704x^71+106x^72+32x^73+24x^74+7x^76+1x^136

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 0.394 seconds.