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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+78x^91+216x^92+8x^93+138x^94+144x^95+12x^96+30x^97+72x^98+2x^99+24x^100+4x^111

The gray image is a linear code over GF(3) with n=423, k=6 and d=273.
This code was found by Heurico 1.16 in 0.0364 seconds.