The generator matrix

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

generates a code of length 34 over Z8 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+80x^27+278x^28+776x^29+756x^30+1544x^31+1645x^32+2194x^33+1776x^34+2232x^35+1738x^36+1658x^37+708x^38+552x^39+226x^40+166x^41+24x^42+8x^43+16x^44+6x^45

The gray image is a code over GF(2) with n=136, k=14 and d=54.
This code was found by Heurico 1.11 in 1.77 seconds.