The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+66x^42+582x^44+272x^45+324x^46+1842x^47+498x^48+648x^49+1872x^50+348x^51+66x^53+22x^54+12x^56+6x^57+2x^63

The gray image is a linear code over GF(3) with n=216, k=8 and d=126.
This code was found by Heurico 1.16 in 0.0415 seconds.