The generator matrix

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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+1104x^138+1182x^139+1428x^140+2682x^141+1746x^142+1536x^143+2152x^144+1284x^145+978x^146+1620x^147+1098x^148+690x^149+1014x^150+498x^151+222x^152+400x^153+24x^154+6x^155+6x^156+6x^159+6x^162

The gray image is a linear code over GF(3) with n=648, k=9 and d=414.
This code was found by Heurico 1.16 in 1.04 seconds.