The generator matrix

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

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+196x^138+228x^139+972x^140+466x^141+558x^142+828x^143+572x^144+414x^145+630x^146+434x^147+366x^148+576x^149+172x^150+54x^151+72x^152+12x^156+4x^159+4x^171+2x^180

The gray image is a linear code over GF(3) with n=648, k=8 and d=414.
This code was found by Heurico 1.16 in 0.268 seconds.