The generator matrix

 1  1  1  1  1  1  1  X
 0  X  0 2X^2+X 2X  0 2X^2 2X^2+X
 0  0  X X^2+2X  0 X^2 2X^2+X X^2+2X
 0  0  0 X^2 X^2 X^2 2X^2 2X^2

generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+120x^11+92x^12+882x^14+320x^15+2916x^16+1764x^17+296x^18+150x^20+16x^21+4x^24

The gray image is a linear code over GF(3) with n=72, k=8 and d=33.
This code was found by Heurico 1.16 in 0.0114 seconds.