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

generates a code of length 52 over Z3[X]/(X^3) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+288x^101+124x^102+1512x^104+72x^105+44x^108+144x^110+2x^156

The gray image is a linear code over GF(3) with n=468, k=7 and d=303.
This code was found by Heurico 1.16 in 13.2 seconds.