The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+220x^27+625x^28+1302x^29+1836x^30+2896x^31+3158x^32+4138x^33+4050x^34+4578x^35+3325x^36+2856x^37+1794x^38+1144x^39+493x^40+242x^41+62x^42+22x^43+14x^44+6x^45+2x^46+4x^47

The gray image is a code over GF(2) with n=136, k=15 and d=54.
This code was found by Heurico 1.16 in 13.9 seconds.