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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+78x^93+84x^95+256x^96+36x^97+126x^98+488x^99+252x^100+198x^101+958x^102+1332x^103+1704x^104+2536x^105+2394x^106+3204x^107+2640x^108+1692x^109+270x^110+570x^111+126x^112+156x^113+288x^114+72x^116+98x^117+18x^119+36x^120+28x^123+18x^126+14x^129+4x^132+4x^135+2x^141

The gray image is a linear code over GF(3) with n=477, k=9 and d=279.
This code was found by Heurico 1.16 in 1.79 seconds.