The generator matrix

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

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+42x^42+24x^44+166x^45+252x^46+102x^47+908x^48+792x^49+3180x^50+3568x^51+4302x^52+12078x^53+6766x^54+7524x^55+11994x^56+4796x^57+1638x^58+276x^59+382x^60+72x^61+48x^62+74x^63+38x^66+22x^69+4x^72

The gray image is a linear code over GF(3) with n=243, k=10 and d=126.
This code was found by Heurico 1.16 in 3.14 seconds.