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

generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+268x^138+450x^141+162x^142+1384x^144+648x^145+2386x^147+648x^148+238x^150+138x^153+116x^156+68x^159+50x^162+2x^165+2x^207

The gray image is a linear code over GF(3) with n=657, k=8 and d=414.
This code was found by Heurico 1.16 in 1.55 seconds.