The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+92x^6+54x^8+472x^9+648x^10+432x^11+2832x^12+3888x^13+4212x^14+7328x^15+16524x^16+7560x^17+7384x^18+5184x^19+864x^20+1488x^21+86x^24

The gray image is a linear code over GF(3) with n=24, k=10 and d=6.
This code was found by Heurico 1.16 in 0.417 seconds.