The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+28x^39+82x^42+162x^44+46x^45+324x^47+32x^48+32x^54+10x^57+8x^60+2x^63+2x^66

The gray image is a linear code over GF(3) with n=69, k=6 and d=39.
This code was found by Heurico 1.16 in 0.00561 seconds.