The generator matrix

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

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+10x^21+72x^22+84x^23+378x^24+198x^25+1986x^26+1754x^27+7128x^28+7632x^29+15124x^30+14130x^31+7602x^32+2304x^33+234x^34+192x^35+90x^36+108x^37+22x^39

The gray image is a linear code over GF(3) with n=135, k=10 and d=63.
This code was found by Heurico 1.16 in 1.21 seconds.