The generator matrix

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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+90x^102+198x^103+58x^105+1620x^106+44x^108+54x^109+18x^111+72x^112+30x^114+2x^159

The gray image is a linear code over GF(3) with n=477, k=7 and d=306.
This code was found by Heurico 1.16 in 0.184 seconds.