The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  X
 0 X^2  0  0  0  0 X^2 2X^2 2X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 2X^2  0  0 X^2 X^2
 0  0 X^2  0  0 X^2 2X^2  0 2X^2  0 X^2 X^2 2X^2 2X^2  0 X^2  0  0 X^2 X^2 X^2 2X^2 2X^2 2X^2
 0  0  0 X^2  0 2X^2 2X^2 X^2  0 X^2 X^2  0  0 X^2 2X^2 X^2 X^2 X^2  0 X^2 X^2  0 2X^2  0
 0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0  0 2X^2 2X^2  0 X^2 2X^2 2X^2 X^2  0  0 X^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+64x^42+54x^44+64x^45+216x^47+1494x^48+216x^50+24x^51+8x^54+32x^57+2x^60+8x^63+4x^66

The gray image is a linear code over GF(3) with n=216, k=7 and d=126.
This code was found by Heurico 1.16 in 0.0155 seconds.