The generator matrix

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

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+192x^14+94x^15+1728x^16+1152x^17+5398x^18+6912x^19+24336x^20+10636x^21+6912x^22+1536x^23+140x^24+10x^27+2x^30

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 0.549 seconds.