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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+106x^78+90x^80+334x^81+18x^82+174x^83+446x^84+144x^85+702x^86+580x^87+3348x^88+2214x^89+638x^90+6408x^91+2226x^92+766x^93+288x^94+270x^95+438x^96+126x^98+208x^99+30x^101+52x^102+40x^105+14x^108+14x^111+4x^114+2x^117+2x^123

The gray image is a linear code over GF(3) with n=405, k=9 and d=234.
This code was found by Heurico 1.16 in 1.46 seconds.