The generator matrix

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

generates a code of length 52 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+366x^96+162x^97+720x^98+922x^99+594x^100+1818x^101+1570x^102+1620x^103+3348x^104+1990x^105+1620x^106+2466x^107+1326x^108+378x^109+396x^110+228x^111+106x^114+22x^117+18x^120+4x^123+6x^126+2x^129

The gray image is a linear code over GF(3) with n=468, k=9 and d=288.
This code was found by Heurico 1.16 in 1.48 seconds.