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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 98.

Homogenous weight enumerator: w(x)=1x^0+570x^98+618x^99+2238x^100+2946x^101+2858x^102+5448x^103+5832x^104+4554x^105+7566x^106+6288x^107+4816x^108+6354x^109+4188x^110+1744x^111+1626x^112+972x^113+176x^114+66x^115+72x^116+46x^117+30x^118+30x^119+6x^120+4x^123

The gray image is a linear code over GF(3) with n=477, k=10 and d=294.
This code was found by Heurico 1.16 in 5.87 seconds.