The generator matrix

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

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+108x^14+144x^15+810x^16+648x^17+60x^18+3240x^19+10044x^20+240x^21+3240x^22+864x^23+180x^24+20x^27+24x^30

The gray image is a linear code over GF(3) with n=90, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0847 seconds.