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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+172x^96+178x^99+270x^102+648x^105+4374x^106+494x^108+216x^111+84x^114+34x^117+62x^123+20x^126+6x^132+2x^144

The gray image is a linear code over GF(3) with n=477, k=8 and d=288.
This code was found by Heurico 1.16 in 82.7 seconds.