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

generates a code of length 52 over Z3[X]/(X^3) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+168x^97+222x^98+36x^99+480x^100+240x^101+712x^102+1020x^103+678x^104+1392x^105+972x^106+102x^107+34x^108+108x^109+108x^110+2x^111+96x^112+78x^113+6x^114+48x^115+18x^116+2x^117+24x^118+12x^119+2x^144

The gray image is a linear code over GF(3) with n=468, k=8 and d=291.
This code was found by Heurico 1.16 in 1.01 seconds.