The generator matrix

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

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+172x^36+18x^38+162x^39+180x^41+306x^42+720x^44+282x^45+1440x^47+324x^48+1440x^50+252x^51+576x^53+398x^54+162x^57+90x^60+38x^63

The gray image is a linear code over GF(3) with n=72, k=8 and d=36.
This code was found by Heurico 1.16 in 3.77 seconds.