The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 0 1 1 1 1 1 2X 1 X 1 X 1 1 1 2X 0 1 1 1 1 1 0 X X 1 1 1 0 1 1 1 0 1 X 2X X 1 2X 1 1 X 1 1 1 1 1 1 0 0 0 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 X+1 1 0 2 2X+1 X+1 2 1 X+2 1 2 1 0 X+2 X 1 1 2X 2X X+2 1 X+2 1 1 1 2X+1 1 X 1 2X+2 2X 1 1 2X+2 1 1 1 2X+2 1 X+2 1 1 X 2X+2 0 1 2X+1 2 1 1 1 X+1 2X+1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 0 X X 2X 0 X X X 0 2X 2X 2X X X 0 X X 0 0 2X X X 0 0 2X 0 0 2X 0 X 0 X X 0 X 0 2X X 2X 2X X X 2X X 0 0 2X 2X 0 0 X 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 2X 2X 2X 2X X X X 2X 0 X 0 X 2X 2X X 2X X 2X 0 0 2X 0 2X X X X 2X 2X X X 0 X 2X X 0 X 0 2X 0 0 0 2X 2X 2X 0 2X 0 X 0 2X 0 X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 X X 2X 0 X 0 2X 2X X X X 2X X 0 X 2X X X X 2X X X X 2X 2X X 2X 0 2X X 2X X X X X X 2X X 2X X 2X 0 0 X 2X 0 0 X 2X 2X X X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 X X 0 0 2X 0 X 2X 2X 2X 2X 0 X 0 0 0 2X 2X 0 2X X X 2X X X 2X X X X 0 0 0 X 0 X 2X 0 2X 0 2X 0 X X 2X 2X 0 X X X X X 0
generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 132.
Homogenous weight enumerator: w(x)=1x^0+262x^132+66x^133+72x^134+366x^135+138x^136+198x^137+478x^138+240x^139+240x^140+482x^141+228x^142+216x^143+554x^144+264x^145+306x^146+544x^147+240x^148+294x^149+376x^150+192x^151+90x^152+312x^153+84x^154+36x^155+148x^156+6x^157+6x^158+52x^159+24x^162+12x^165+14x^168+8x^171+6x^174+4x^180+2x^186
The gray image is a linear code over GF(3) with n=216, k=8 and d=132.
This code was found by Heurico 1.16 in 10.9 seconds.