The generator matrix

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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+86x^96+150x^97+780x^98+906x^99+1710x^100+2604x^101+2474x^102+4698x^103+5190x^104+5568x^105+8100x^106+7104x^107+5836x^108+6102x^109+3888x^110+1540x^111+936x^112+582x^113+230x^114+120x^115+180x^116+70x^117+36x^118+78x^119+54x^120+18x^121+6x^122+2x^123

The gray image is a linear code over GF(3) with n=477, k=10 and d=288.
This code was found by Heurico 1.16 in 7.43 seconds.