The generator matrix

 1  0  0  1  1  1 2X 2X^2+X
 0  1  0 2X^2+2X+1  X 2X^2+X+1  1 2X^2+2X
 0  0  1 2X^2+2X+2  X 2X^2+X+2 2X  1
 0  0  0 2X^2 X^2  0 X^2 X^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+144x^11+2038x^12+4104x^14+8088x^15+28188x^16+8208x^17+8084x^18+180x^20+8x^21+6x^24

The gray image is a linear code over GF(3) with n=72, k=10 and d=33.
This code was found by Heurico 1.16 in 143 seconds.