The generator matrix

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

generates a code of length 20 over Z3[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+192x^32+176x^33+216x^34+930x^35+2442x^36+1296x^37+8688x^38+9122x^39+6966x^40+16170x^41+9032x^42+1728x^43+1554x^44+312x^45+168x^47+38x^48+8x^51+8x^54+2x^57

The gray image is a linear code over GF(3) with n=180, k=10 and d=96.
This code was found by Heurico 1.16 in 2.46 seconds.