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  X  1  1  1  1  1  1  X  1  X  1  0  1  1  1  0  1
 0  X  0  0 2X 2X^2+X 2X^2+2X  X 2X X^2  X  X 2X^2+2X 2X^2+X  0 X^2 2X^2+2X 2X X^2 2X^2+X X^2 2X^2 2X^2+2X 2X^2+X  X 2X X^2+2X X^2 X^2+X 2X^2+2X 2X^2 2X^2+X 2X^2+2X X^2 X^2+X 2X^2+2X 2X^2+X X^2+2X X^2 2X  0 X^2+X  0  X 2X^2 2X X^2 X^2+2X 2X^2 X^2+2X  X 2X^2 X^2 2X^2 2X  X 2X^2+X  0 2X^2+X X^2+X  X 2X^2+X 2X^2+X 2X^2+X 2X^2  0 2X  X 2X^2+X 2X^2+2X 2X^2+2X  X 2X^2+X
 0  0  X 2X X^2 2X^2+2X X^2+X  X 2X^2+2X 2X^2 X^2+X 2X^2 X^2+X 2X  X 2X  0 2X 2X^2 2X^2 X^2+2X 2X^2+X  0 2X^2+2X X^2+X X^2+X X^2+2X X^2+2X X^2+2X  X  X  X X^2 X^2 X^2 X^2 X^2+X X^2+2X X^2 X^2+2X X^2+X X^2+2X X^2 2X^2+2X 2X^2+2X 2X^2 2X^2+2X 2X^2 2X^2+X 2X^2+X X^2 2X^2+2X 2X^2+2X 2X^2 2X^2+X X^2+2X X^2+2X 2X^2+2X  0 X^2 X^2+2X 2X^2+2X  X  0 2X 2X^2+X  0 2X^2 X^2+X 2X^2+X  X 2X 2X^2
 0  0  0 X^2  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2  0 2X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2  0 X^2 2X^2  0 X^2 X^2  0  0 X^2 X^2 2X^2  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2  0 2X^2 X^2  0 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 2X^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+54x^138+174x^139+186x^140+212x^141+498x^142+138x^143+484x^144+1278x^145+870x^146+732x^147+1206x^148+156x^149+68x^150+96x^151+42x^152+62x^153+48x^154+24x^155+36x^156+78x^157+18x^158+36x^159+18x^160+18x^161+14x^162+6x^163+6x^164+2x^204

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 0.436 seconds.