The generator matrix

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

generates a code of length 21 over Z3[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+462x^37+486x^38+1762x^39+2748x^40+1764x^41+3526x^42+4578x^43+1770x^44+1742x^45+786x^46+24x^47+14x^48+12x^49+6x^50+2x^51

The gray image is a linear code over GF(3) with n=189, k=9 and d=111.
This code was found by Heurico 1.16 in 0.218 seconds.