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

generates a code of length 51 over Z3[X]/(X^3) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+570x^93+54x^94+54x^95+1086x^96+108x^97+432x^98+1588x^99+2268x^100+1134x^101+3228x^102+4644x^103+1080x^104+1556x^105+216x^106+216x^107+724x^108+480x^111+182x^114+52x^117+6x^120+2x^123+2x^135

The gray image is a linear code over GF(3) with n=459, k=9 and d=279.
This code was found by Heurico 1.16 in 5.64 seconds.