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

generates a code of length 74 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+468x^138+1140x^141+1316x^144+1944x^146+1638x^147+5832x^148+3888x^149+1542x^150+680x^153+552x^156+390x^159+206x^162+60x^165+24x^168+2x^216

The gray image is a linear code over GF(3) with n=666, k=9 and d=414.
This code was found by Heurico 1.16 in 4.31 seconds.