The generator matrix

 1  0  1  1  1  1  1  X 2X  1  1  1  1 2X^2  1  1  X  1  1  1  1  1  1  1 2X^2+2X  1  1  1 2X^2+X  1  1  1  1  0  1 X^2+X  1  1 X^2  1  1  1  1  1  0  1 2X^2  1  1  1  1 X^2+2X  1  1 X^2+X  1  1  1  1 2X^2+2X X^2+X  1  1  X  1  1
 0  1  1  2 2X^2 2X+1  2  1  1  2 2X^2+2X+1 2X^2+X X+1  1 2X^2 X+2  1 X^2+2X X^2+2X+2 2X^2+X+1 2X^2 X+2 X^2+X+1 2X^2+2X  1 2X^2+1 2X^2+X+2  X  1 X+2 2X^2+2X+1 2X^2+X+1 X^2+2X  1 X^2+X+2  1 2X^2+2 X^2+X+2  1  1 X+1 2X^2  X X+2  1 X^2+2X  1 X^2+2X+1 X+1 2X^2+X+1 X^2+X  1 X^2+2X 2X^2+1  1 2X^2+2X+2 X^2+2 2X^2+2X+1 2X^2+X  1  1  0 X^2+2 X^2+X 2X^2+1 X+2
 0  0 2X  0 2X^2  0  0 X^2  0 2X^2 2X^2 X^2 X^2 X^2+X  X 2X^2+2X 2X 2X X^2+X X^2+X 2X^2+X 2X^2+X 2X 2X X^2+2X X^2+X X^2+X 2X^2+2X 2X^2+X X^2+2X  X 2X 2X^2+X X^2+X X^2+2X 2X 2X^2+X  0 X^2+2X 2X X^2  X  X X^2+X 2X 2X^2  0 X^2+2X 2X^2 X^2+2X  X X^2 X^2+X  X X^2 2X^2 2X X^2+2X 2X^2+2X X^2+2X 2X^2 2X^2+2X  X 2X^2+X X^2 X^2
 0  0  0  X 2X^2+X X^2+X X^2  X X^2+2X X^2+2X 2X^2+2X 2X 2X^2 X^2+2X X^2 X^2+X 2X 2X^2+X 2X^2+2X X^2 2X^2+2X 2X^2  X 2X^2  0 2X  X X^2+2X 2X^2 X^2 2X^2+X 2X^2+2X 2X 2X^2+X 2X^2+2X  X 2X^2 X^2 2X^2+2X X^2+X X^2 X^2+X 2X^2 2X X^2 2X^2+2X  X 2X X^2+X  0 X^2+X 2X^2  0 2X^2+2X 2X X^2+2X X^2 2X^2+2X 2X 2X^2+X 2X X^2 2X^2  X 2X^2+2X  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+288x^122+462x^123+450x^124+1800x^125+2372x^126+1998x^127+3492x^128+4290x^129+3942x^130+6324x^131+6312x^132+6138x^133+6288x^134+5646x^135+3078x^136+2742x^137+1662x^138+432x^139+540x^140+192x^141+228x^143+124x^144+96x^146+60x^147+48x^149+18x^150+18x^152+2x^153+6x^155

The gray image is a linear code over GF(3) with n=594, k=10 and d=366.
This code was found by Heurico 1.16 in 9.62 seconds.