The generator matrix

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

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+1782x^16+648x^17+5892x^18+7128x^19+23166x^20+11904x^21+7128x^22+864x^23+180x^24+20x^27+24x^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 0.362 seconds.