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

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+276x^122+296x^123+18x^124+738x^125+488x^126+144x^127+1710x^128+964x^129+918x^130+3756x^131+1594x^132+1548x^133+3756x^134+1242x^135+288x^136+702x^137+220x^138+342x^140+136x^141+240x^143+76x^144+108x^146+56x^147+36x^149+26x^150+2x^153+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 3.46 seconds.