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

generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+116x^129+198x^132+228x^135+18x^136+238x^138+180x^139+210x^141+720x^142+184x^144+1440x^145+13122x^146+166x^147+1440x^148+164x^150+576x^151+136x^153+134x^156+118x^159+96x^162+78x^165+58x^168+24x^171+24x^174+6x^177+6x^180+2x^204

The gray image is a linear code over GF(3) with n=657, k=9 and d=387.
This code was found by Heurico 1.16 in 75.1 seconds.