The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+48x^20+104x^21+108x^22+318x^23+360x^24+288x^25+3756x^26+710x^27+4968x^28+6918x^29+752x^30+432x^31+600x^32+234x^33+36x^34+24x^35+18x^36+8x^39

The gray image is a linear code over GF(3) with n=126, k=9 and d=60.
This code was found by Heurico 1.16 in 0.25 seconds.