The generator matrix

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

generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+78x^6+54x^8+372x^9+162x^10+324x^11+1674x^12+648x^13+1728x^14+5064x^15+3888x^16+4968x^17+17388x^18+7128x^19+5184x^20+6696x^21+1296x^22+864x^23+1446x^24+86x^27

The gray image is a linear code over GF(3) with n=27, k=10 and d=6.
This code was found by Heurico 1.16 in 0.385 seconds.