The generator matrix

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

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+54x^25+840x^26+1272x^27+1710x^28+2664x^29+5478x^30+3330x^31+2952x^32+1254x^33+90x^34+24x^35+14x^36

The gray image is a linear code over GF(3) with n=135, k=9 and d=75.
This code was found by Heurico 1.16 in 0.194 seconds.