The generator matrix

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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+518x^108+216x^109+108x^110+1732x^111+702x^112+648x^113+3014x^114+1458x^115+1296x^116+4040x^117+1404x^118+864x^119+2526x^120+594x^121+390x^123+104x^126+40x^129+16x^132+6x^135+4x^138+2x^144

The gray image is a linear code over GF(3) with n=522, k=9 and d=324.
This code was found by Heurico 1.16 in 1.68 seconds.