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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+108x^123+288x^124+390x^125+828x^126+918x^127+1062x^128+1372x^129+1410x^130+1908x^131+2242x^132+2058x^133+2094x^134+1908x^135+1338x^136+780x^137+428x^138+264x^139+54x^140+76x^141+30x^142+18x^143+54x^144+12x^145+12x^146+16x^147+2x^150+8x^153+2x^156+2x^168

The gray image is a linear code over GF(3) with n=594, k=9 and d=369.
This code was found by Heurico 1.16 in 1.28 seconds.