The generator matrix

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

generates a code of length 14 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+60x^21+54x^22+458x^24+324x^25+4860x^26+1484x^27+648x^28+9720x^29+1518x^30+432x^31+98x^33+18x^36+6x^39+2x^42

The gray image is a linear code over GF(3) with n=126, k=9 and d=63.
This code was found by Heurico 1.16 in 0.603 seconds.