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

generates a code of length 52 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+194x^96+430x^99+932x^102+2916x^104+1518x^105+224x^108+158x^111+138x^114+36x^117+8x^120+4x^123+2x^153

The gray image is a linear code over GF(3) with n=468, k=8 and d=288.
This code was found by Heurico 1.16 in 0.273 seconds.