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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 122.

Homogenous weight enumerator: w(x)=1x^0+264x^122+240x^123+798x^125+488x^126+414x^127+1356x^128+1206x^129+1188x^130+2448x^131+2778x^132+2214x^133+2514x^134+1288x^135+558x^136+570x^137+234x^138+372x^140+198x^141+282x^143+68x^144+108x^146+52x^147+30x^149+6x^150+6x^152+2x^174

The gray image is a linear code over GF(3) with n=594, k=9 and d=366.
This code was found by Heurico 1.16 in 22.4 seconds.