The generator matrix

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

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+458x^24+414x^25+1788x^26+2644x^27+6372x^28+6840x^29+17006x^30+12582x^31+6876x^32+3358x^33+558x^34+48x^35+100x^36+4x^39

The gray image is a linear code over GF(3) with n=135, k=10 and d=72.
This code was found by Heurico 1.16 in 1.15 seconds.