The generator matrix

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

generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+76x^9+162x^10+780x^12+972x^13+7290x^14+2760x^15+28188x^16+14580x^17+2776x^18+1296x^19+156x^21+12x^24

The gray image is a linear code over GF(3) with n=72, k=10 and d=27.
This code was found by Heurico 1.16 in 0.264 seconds.