The generator matrix

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

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+546x^96+450x^97+2124x^98+3384x^99+2574x^100+6102x^101+5726x^102+3006x^103+8118x^104+7582x^105+4032x^106+6570x^107+4366x^108+1476x^109+1836x^110+790x^111+126x^112+36x^113+150x^114+34x^117+18x^120+2x^123

The gray image is a linear code over GF(3) with n=468, k=10 and d=288.
This code was found by Heurico 1.16 in 5.96 seconds.