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  X  X  0  X  X  0  X  X X^2  1  1  1  1  X  X X^2  X  1  1  X  X
 0  X 2X  0 2X^2+X 2X X^2 2X^2+X X^2+2X X^2 X^2+X X^2+2X X^2  0 X^2+X  X 2X X^2+2X 2X^2 2X^2 2X^2+X X^2+X 2X^2+2X 2X^2+2X 2X^2  X 2X^2+2X 2X^2+X 2X  X 2X^2+X 2X  X X^2+X X^2+2X  X  0  0 X^2 X^2 X^2+X X^2+2X  X X^2+2X  0 X^2 2X X^2
 0  0 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 X^2  0 X^2  0 2X^2 X^2 2X^2  0 2X^2  0 X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0 2X^2  0 X^2 X^2 X^2  0  0 2X^2 2X^2  0 X^2 2X^2 X^2 X^2 X^2 X^2  0 2X^2  0 2X^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+60x^93+246x^94+128x^96+162x^97+32x^99+72x^100+18x^102+6x^103+4x^114

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 0.0392 seconds.