The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 X 1 1 1 1 1 1 2X 1 0 1 1 1 X 1 2X 1 0 1 1 1 1 0 1 1 1 1 2X 2X 1 X 1 1 1 0 1 1 X 1 1 1 1 1 1 1 2X 1 X 1 X 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 0 2 1 2X+1 1 2X+1 2X+2 0 X+1 X 2 1 2 1 0 2X+1 0 1 X 1 2 1 X+2 2X+1 2X 1 1 X 2X 2 1 1 1 0 1 2X X+1 X+1 1 2X 2X 1 2X+1 0 1 2X+2 X+2 1 2 1 X 1 2X+2 1 X+1 X 2X+1
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 0 X X X X 2X 2X 2X 0 X 2X X 2X X 2X 2X 0 X 2X X 0 2X 2X 0 2X 2X X 0 2X 2X X 2X 2X 2X 2X 2X X 2X 0 0 X 0 X 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 2X X X
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 0 X 2X 2X X 0 2X X 0 2X X 2X 2X 2X X X 0 X 0 2X X 0 2X X 2X X X X 0 X 2X 0 2X 2X X 2X 0 0 2X X 2X 0 2X X 0 2X X X X 2X 0 X 0 0 2X 2X X
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X X X 0 X 0 2X 2X 2X 2X 0 0 X 0 X X X X 0 X 0 X X X 0 2X 2X X 2X 0 X 2X X 0 X 0 X 2X 0 2X 2X 0 0 X 0 2X X 0 0 X 2X 2X X 2X X X X X 2X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 0 0 2X 0 X X X 0 2X 0 X 2X 0 X 2X X 0 X 0 X 0 X 0 2X 2X X 2X X 2X X 0 0 0 2X 2X X 0 0 X X 0 2X 0 0 0 X 2X X 0 X 2X 2X X 2X X 0 X 0
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 0 X 2X 2X X 0 2X 2X X 0 2X 0 X X X 0 2X 0 X 2X X X 0 X X 2X 2X 0 0 X 0 2X X 0 0 X X 2X X X 0 2X 2X 2X 0 0 2X 2X X X X 0 X X X X 2X X
generates a code of length 73 over Z3[X]/(X^2) who´s minimum homogenous weight is 128.
Homogenous weight enumerator: w(x)=1x^0+6x^128+124x^129+60x^130+60x^131+192x^132+264x^133+264x^134+242x^135+594x^136+624x^137+204x^138+942x^139+966x^140+224x^141+1122x^142+1458x^143+194x^144+1410x^145+1686x^146+166x^147+1632x^148+1722x^149+172x^150+1320x^151+1224x^152+112x^153+960x^154+492x^155+146x^156+330x^157+222x^158+102x^159+102x^160+24x^161+90x^162+6x^163+96x^165+6x^166+52x^168+34x^171+20x^174+14x^177+2x^180
The gray image is a linear code over GF(3) with n=219, k=9 and d=128.
This code was found by Heurico 1.16 in 47.5 seconds.