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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+54x^93+162x^94+12x^96+6x^99+6x^102+2x^117

The gray image is a linear code over GF(3) with n=423, k=5 and d=279.
This code was found by Heurico 1.16 in 0.045 seconds.