The generator matrix

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

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+68x^36+120x^39+54x^40+98x^42+324x^43+100x^45+648x^46+108x^48+432x^49+98x^51+72x^54+42x^57+20x^60+2x^63

The gray image is a linear code over GF(3) with n=69, k=7 and d=36.
This code was found by Heurico 1.16 in 0.0347 seconds.