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

generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+234x^136+390x^137+114x^138+438x^139+684x^140+228x^141+918x^142+1092x^143+1564x^144+1644x^145+4590x^146+2796x^147+1740x^148+1230x^149+236x^150+318x^151+282x^152+92x^153+258x^154+222x^155+40x^156+168x^157+168x^158+20x^159+78x^160+48x^161+8x^162+24x^163+36x^164+2x^165+12x^166+6x^167+2x^204

The gray image is a linear code over GF(3) with n=657, k=9 and d=408.
This code was found by Heurico 1.16 in 4.82 seconds.