The generator matrix

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

generates a code of length 72 over Z3[X]/(X^3) who�s minimum homogenous weight is 131.

Homogenous weight enumerator: w(x)=1x^0+126x^131+156x^132+180x^133+504x^134+344x^135+918x^136+1752x^137+1224x^138+2556x^139+4350x^140+1970x^141+5598x^142+7026x^143+3420x^144+6930x^145+7734x^146+2430x^147+4572x^148+3726x^149+1014x^150+1026x^151+768x^152+164x^153+90x^154+180x^155+104x^156+60x^158+28x^159+18x^161+28x^162+20x^165+10x^168+10x^171+2x^174+6x^177+2x^180+2x^186

The gray image is a linear code over GF(3) with n=648, k=10 and d=393.
This code was found by Heurico 1.16 in 16.1 seconds.