The generator matrix

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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+162x^121+222x^122+426x^123+1092x^124+1548x^125+1506x^126+2634x^127+3186x^128+3554x^129+5550x^130+5976x^131+5424x^132+6864x^133+6084x^134+4364x^135+4230x^136+2742x^137+1200x^138+1002x^139+516x^140+136x^141+204x^142+72x^143+110x^144+66x^145+48x^146+28x^147+54x^148+18x^149+6x^150+12x^151+4x^153+4x^156+2x^159+2x^165

The gray image is a linear code over GF(3) with n=594, k=10 and d=363.
This code was found by Heurico 1.16 in 10.3 seconds.