The generator matrix

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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+72x^97+270x^98+204x^99+666x^100+780x^101+392x^102+2556x^103+1470x^104+558x^105+4626x^106+1842x^107+670x^108+3384x^109+1158x^110+290x^111+360x^112+222x^113+36x^114+66x^116+14x^117+24x^119+10x^120+2x^126+8x^129+2x^138

The gray image is a linear code over GF(3) with n=477, k=9 and d=291.
This code was found by Heurico 1.16 in 0.966 seconds.