The generator matrix

 1  0  1  1  1  6  1  1  4  1  1  2  1  1  0  1  1  6  1  1  4  1  1  2  1  1  0  1  1  6  1  1  1  1  4  2  1  1  2  2  0  2  4  2  1  1  0  4  1  1  1  1  6  2  2  2  2  2  0  4  1  1  1  1  1  1  1  1
 0  1  3  6  5  1  4  7  1  2  1  1  0  3  1  6  5  1  4  7  1  2  1  1  0  3  1  6  5  1  4  7  2  1  1  1  0  6  0  6  2  2  2  4  3  7  1  1  4  2  5  1  1  1  0  4  6  2  2  2  0  4  3  7  6  2  0  4

generates a code of length 68 over Z8 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+49x^68+4x^70+4x^72+4x^74+1x^76+1x^80

The gray image is a code over GF(2) with n=272, k=6 and d=136.
This code was found by Heurico 1.16 in 0.0775 seconds.