The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+20x^9+18x^10+154x^12+108x^13+162x^14+496x^15+216x^16+324x^17+492x^18+144x^19+44x^21+8x^24

The gray image is a linear code over GF(3) with n=24, k=7 and d=9.
This code was found by Heurico 1.16 in 0.00227 seconds.