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

generates a code of length 52 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+372x^102+234x^105+94x^108+24x^111+2x^117+2x^126

The gray image is a linear code over GF(3) with n=468, k=6 and d=306.
This code was found by Heurico 1.16 in 1.42 seconds.