The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2  0  0  0  0 X^2 X^2 2X^2 X^2  0 2X^2 2X^2  0
 0  0 X^2  0  0 X^2 2X^2 2X^2  0  0 X^2 X^2 2X^2  0
 0  0  0 X^2  0 2X^2 2X^2 2X^2  0 2X^2 2X^2  0 2X^2 2X^2
 0  0  0  0 X^2 2X^2 2X^2  0 X^2 X^2  0 2X^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+34x^21+50x^24+50x^27+1944x^28+46x^30+38x^33+12x^36+10x^39+2x^42

The gray image is a linear code over GF(3) with n=126, k=7 and d=63.
This code was found by Heurico 1.16 in 0.0277 seconds.