The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+22x^42+94x^45+112x^48+162x^50+104x^51+648x^53+4478x^54+648x^56+84x^57+92x^60+54x^63+36x^66+16x^69+8x^72+2x^75

The gray image is a linear code over GF(3) with n=243, k=8 and d=126.
This code was found by Heurico 1.16 in 0.118 seconds.