The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+22x^42+24x^45+162x^46+18x^48+12x^51+2x^54+2x^69

The gray image is a linear code over GF(3) with n=69, k=5 and d=42.
This code was found by Heurico 1.16 in 0.00217 seconds.