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

generates a code of length 31 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+30x^54+58x^57+220x^60+354x^63+14x^66+8x^69+18x^72+18x^75+6x^78+2x^90

The gray image is a linear code over GF(3) with n=93, k=6 and d=54.
This code was found by Heurico 1.16 in 0.00914 seconds.