The generator matrix

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

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+66x^13+1704x^14+904x^15+12384x^16+8928x^17+71878x^18+49068x^19+181152x^20+142216x^21+49128x^22+12336x^23+1508x^24+162x^25+4x^27+2x^30

The gray image is a linear code over GF(3) with n=90, k=12 and d=39.
This code was found by Heurico 1.16 in 36.4 seconds.