The generator matrix

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

generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+330x^54+324x^60+36x^63+36x^72+2x^81

The gray image is a linear code over GF(3) with n=87, k=6 and d=54.
This code was found by Heurico 1.16 in 0.487 seconds.