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

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+112x^96+150x^97+258x^98+462x^99+408x^100+534x^101+882x^102+618x^103+2250x^104+2418x^105+2568x^106+3894x^107+2426x^108+678x^109+480x^110+328x^111+204x^112+156x^113+266x^114+144x^115+132x^116+130x^117+84x^118+48x^119+20x^120+6x^121+24x^122+2x^144

The gray image is a linear code over GF(3) with n=477, k=9 and d=288.
This code was found by Heurico 1.16 in 1.54 seconds.