The generator matrix

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

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+362x^12+2664x^14+1400x^15+8262x^16+5328x^17+1376x^18+150x^20+16x^21+4x^24

The gray image is a linear code over GF(3) with n=72, k=9 and d=33.
This code was found by Heurico 1.16 in 2.86 seconds.