The generator matrix

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

generates a code of length 21 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+52x^36+48x^38+126x^39+216x^40+36x^41+1052x^42+432x^43+54x^44+64x^45+24x^47+72x^48+8x^51+2x^60

The gray image is a linear code over GF(3) with n=189, k=7 and d=108.
This code was found by Heurico 1.16 in 0.00989 seconds.