The generator matrix

 1  0  1  1  1  1  1  1  1  1
 0  1  1  2 2X+1 2X^2 2X^2+X 2X^2+2  2  0
 0  0 2X  0  X 2X^2+X 2X^2+2X 2X^2+X 2X  0
 0  0  0 X^2  0 2X^2 2X^2 2X^2 2X^2  0
 0  0  0  0 X^2 2X^2  0 X^2 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+44x^12+216x^14+342x^15+648x^16+1296x^17+8370x^18+2592x^19+24462x^20+16100x^21+2592x^22+1728x^23+630x^24+26x^27+2x^30

The gray image is a linear code over GF(3) with n=90, k=10 and d=36.
This code was found by Heurico 1.16 in 0.454 seconds.