The generator matrix

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

generates a code of length 21 over Z3[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+132x^38+10x^39+408x^40+462x^41+8x^42+624x^43+480x^44+48x^46+6x^47+2x^48+4x^51+2x^54

The gray image is a linear code over GF(3) with n=189, k=7 and d=114.
This code was found by Heurico 1.16 in 0.00574 seconds.