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

generates a code of length 31 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+138x^45+304x^48+436x^51+678x^54+2022x^57+4792x^60+6134x^63+3512x^66+758x^69+482x^72+256x^75+112x^78+46x^81+8x^84+4x^87

The gray image is a linear code over GF(3) with n=93, k=9 and d=45.
This code was found by Heurico 1.16 in 3.8 seconds.