The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+138x^28+316x^29+580x^30+694x^31+896x^32+932x^33+1116x^34+974x^35+947x^36+580x^37+508x^38+278x^39+143x^40+60x^41+20x^42+2x^43+3x^44+4x^47

The gray image is a code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.11 in 0.571 seconds.