The generator matrix

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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+444x^103+408x^104+8x^105+606x^106+198x^107+8x^108+264x^109+144x^110+4x^111+90x^112+6x^113+4x^114+2x^129

The gray image is a linear code over GF(3) with n=477, k=7 and d=309.
This code was found by Heurico 1.16 in 0.0517 seconds.