The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+34x^39+120x^40+294x^41+118x^42+396x^43+576x^44+126x^45+714x^46+624x^47+172x^48+918x^49+804x^50+154x^51+648x^52+522x^53+74x^54+114x^55+96x^56+28x^57+6x^58+16x^60+6x^63

The gray image is a linear code over GF(3) with n=72, k=8 and d=39.
This code was found by Heurico 1.16 in 0.161 seconds.