The generator matrix

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

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+102x^38+96x^39+240x^40+114x^41+1040x^42+390x^43+30x^44+56x^45+12x^46+54x^47+18x^48+6x^49+24x^50+2x^51+2x^60

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 0.0236 seconds.