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

generates a code of length 28 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+112x^39+240x^42+396x^45+622x^48+486x^50+694x^51+2916x^53+920x^54+5832x^56+1032x^57+3888x^59+960x^60+780x^63+464x^66+204x^69+90x^72+38x^75+8x^78

The gray image is a linear code over GF(3) with n=84, k=9 and d=39.
This code was found by Heurico 1.16 in 3.1 seconds.