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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+230x^120+640x^123+1272x^126+4020x^129+6898x^132+5094x^135+814x^138+428x^141+170x^144+52x^147+16x^150+16x^153+12x^156+10x^159+6x^162+2x^165+2x^171

The gray image is a linear code over GF(3) with n=594, k=9 and d=360.
This code was found by Heurico 1.16 in 23.1 seconds.