The generator matrix

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

generates a code of length 48 over Z3[X]/(X^3) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+138x^93+162x^94+18x^96+324x^97+22x^99+60x^102+4x^117

The gray image is a linear code over GF(3) with n=432, k=6 and d=279.
This code was found by Heurico 1.16 in 2.02 seconds.