The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+48x^23+806x^24+1008x^25+1986x^26+2672x^27+5280x^28+3876x^29+2892x^30+996x^31+84x^32+28x^33+6x^34

The gray image is a linear code over GF(3) with n=126, k=9 and d=69.
This code was found by Heurico 1.16 in 0.133 seconds.