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  2  2  0  2  2  4  2  2  0  4  4  4  0  0  2  2  2  2  0  4  2  2  0  4  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  2  0  0  2  2  4  4  6  6  4  4  6  6  0  4  2  6  0  4  2  6  4  0  6  2  4  0  6  2  4  2  2  0  6  2  6  6  0  4  2  2  2  2  2  4  0  6  4  0  2  2  2  2  0  0  4  4  4  4  0  0  2  2  6  6
 0  0  2  2  4  6  6  4  4  2  6  0  0  6  2  4  0  2  2  0  4  6  6  4  4  6  6  4  0  2  2  0  2  2  4  2  2  0  0  4  2  2  2  6  6  2  6  6  6  6  2  2  4  0  0  4  0  4  4  0  2  6  6  2  2  6  6  2

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

Homogenous weight enumerator: w(x)=1x^0+120x^68+3x^72+3x^80+1x^88

The gray image is a code over GF(2) with n=272, k=7 and d=136.
This code was found by Heurico 1.16 in 0.128 seconds.