The generator matrix

 1  0  0  0  1  1  1 2X^2+2X  1 2X^2 2X  1  1  1
 0  1  0  0 2X^2+2X 2X^2+1 2X+1  1 X^2  1  1 2X 2X+2 X^2+2X
 0  0  1  0 2X^2+2X+1 2X^2+1 2X+2 2X^2+X+1 2X^2+X 2X^2+2X 2X+2 2X^2+2X  2 2X+1
 0  0  0  1 2X^2+2X+2 2X^2+X X+2 2X^2+X+2 X^2+1  1 2X+2  2 X^2+2 X^2+2X+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+366x^20+214x^21+3240x^22+3648x^23+13912x^24+16074x^25+74352x^26+53114x^27+141480x^28+141546x^29+53274x^30+22302x^31+7008x^32+734x^33+126x^34+42x^35+6x^36+2x^39

The gray image is a linear code over GF(3) with n=126, k=12 and d=60.
This code was found by Heurico 1.16 in 68.6 seconds.