The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+1172x^36+4044x^39+9342x^42+16704x^45+17040x^48+8748x^51+1904x^54+84x^57+10x^63

The gray image is a linear code over GF(3) with n=69, k=10 and d=36.
This code was found by Heurico 1.16 in 14.4 seconds.