The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+254x^27+614x^28+1318x^29+1767x^30+2798x^31+3284x^32+4136x^33+4031x^34+4592x^35+3339x^36+2960x^37+1741x^38+1076x^39+493x^40+224x^41+77x^42+42x^43+11x^44+2x^45+6x^47+2x^48

The gray image is a code over GF(2) with n=136, k=15 and d=54.
This code was found by Heurico 1.11 in 6.42 seconds.