The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+100x^33+188x^36+198x^39+162x^40+300x^42+972x^43+318x^45+1944x^46+342x^48+1296x^49+378x^51+206x^54+108x^57+32x^60+16x^63

The gray image is a linear code over GF(3) with n=69, k=8 and d=33.
This code was found by Heurico 1.16 in 0.258 seconds.