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

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+552x^138+36x^140+1034x^141+216x^142+288x^143+1462x^144+1296x^145+864x^146+2294x^147+4050x^148+1152x^149+2180x^150+1728x^151+576x^152+798x^153+464x^156+386x^159+194x^162+92x^165+18x^168+2x^198

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 9.47 seconds.