The generator matrix

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

generates a code of length 21 over Z3[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+6x^32+164x^33+18x^34+60x^35+518x^36+144x^37+3642x^38+1676x^39+6264x^40+14088x^41+3038x^42+12240x^43+14088x^44+2180x^45+288x^46+192x^47+320x^48+92x^51+28x^54+2x^57

The gray image is a linear code over GF(3) with n=189, k=10 and d=96.
This code was found by Heurico 1.16 in 29.5 seconds.