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  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  2  2  2  2  2  2  2  2  4  4  4  4  4  4  4  0  0  0  0  0  0  0  2  1  1  1  1  2  1
 0  4  0  0  0  4  4  4  0  0  0  4  0  4  4  4  0  0  0  4  0  4  4  4  0  0  4  4  0  4  4  0  0  0  4  0  4  4  4  0  0  4  4  0  4  4  0  0  0  4  4  0  4  4  4  4  4  4  0  0  0  0  0  0  0  4  4  0
 0  0  4  0  4  4  4  0  0  0  4  4  4  4  0  0  0  0  4  4  4  4  0  0  0  4  4  0  4  4  0  0  0  4  4  4  4  0  0  0  4  4  0  4  4  0  0  0  4  4  0  4  4  0  0  0  4  4  4  4  0  0  0  0  4  4  0  0
 0  0  0  4  4  0  4  4  0  4  4  0  0  4  4  0  0  4  4  0  0  4  4  0  4  4  0  0  0  4  4  0  4  4  0  0  4  4  0  4  4  0  0  0  4  4  0  4  4  0  0  0  4  4  0  4  4  0  0  4  4  0  0  4  4  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+38x^68+8x^69+4x^70+8x^71+1x^72+4x^74

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 0.102 seconds.