The generator matrix

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

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+288x^14+720x^15+1296x^16+1728x^17+9456x^18+5184x^19+13176x^20+18792x^21+5184x^22+2304x^23+900x^24+20x^27

The gray image is a linear code over GF(3) with n=90, k=10 and d=42.
This code was found by Heurico 1.16 in 69.9 seconds.