The generator matrix

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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+110x^135+150x^136+714x^137+1068x^138+444x^139+1440x^140+1564x^141+852x^142+1860x^143+2760x^144+1128x^145+2322x^146+2250x^147+666x^148+1248x^149+586x^150+120x^151+138x^152+82x^153+18x^154+42x^155+64x^156+24x^157+12x^158+2x^159+6x^162+6x^168+2x^171+2x^174+2x^177

The gray image is a linear code over GF(3) with n=648, k=9 and d=405.
This code was found by Heurico 1.16 in 1.38 seconds.