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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+306x^108+36x^110+1140x^111+54x^112+288x^113+1330x^114+324x^115+1836x^116+1646x^117+5022x^118+3096x^119+1666x^120+432x^121+576x^122+898x^123+566x^126+304x^129+130x^132+26x^135+4x^138+2x^162

The gray image is a linear code over GF(3) with n=531, k=9 and d=324.
This code was found by Heurico 1.16 in 1.84 seconds.