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

generates a code of length 34 over Z8 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+75x^28+16x^30+125x^32+608x^34+116x^36+16x^38+48x^40+16x^44+2x^48+1x^60

The gray image is a code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 8.55 seconds.