The generator matrix

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

generates a code of length 10 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+380x^12+300x^13+1080x^14+1460x^15+2490x^16+2880x^17+6560x^18+9360x^19+8856x^20+7240x^21+9060x^22+4320x^23+4030x^24+660x^25+360x^26+12x^30

The gray image is a linear code over GF(3) with n=30, k=10 and d=12.
This code was found by Heurico 1.16 in 3.11 seconds.