The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+34x^36+78x^39+112x^42+162x^44+100x^45+648x^47+104x^48+648x^50+100x^51+72x^54+68x^57+40x^60+18x^63+2x^66

The gray image is a linear code over GF(3) with n=72, k=7 and d=36.
This code was found by Heurico 1.16 in 0.0347 seconds.