The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 0 1 1 0 1 1 1 2X 1 1 0 1 1 1 X 2X 1 X 1 1 2X 1 1 1 1 2X 1 1 1 X 1 1 X 0 1 1 1 1 0 2X 1 1 X X 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 0 2X+1 2 1 0 2 1 2X+1 0 2X+1 1 1 X 1 2X+1 2 1 1 1 2X 1 2X+2 X+2 1 2X+1 X 2X+1 2X+1 1 2 2X+2 X+2 1 2X+1 0 1 1 2 X+1 X+2 1 1 1 X+2 2X+1 2X X 2X+1 2 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 0 X 2X X 0 X 0 2X 2X 0 X 2X 2X X 2X X X X 0 0 X 2X 0 X 0 0 X 2X X 2X 2X 2X 0 2X 0 0 X 2X 2X X 2X 2X X 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X X 2X 2X X 0 0 X X X 2X X 2X X 0 X 2X 2X 2X X 2X X X X 2X 2X 0 0 2X 2X 0 2X 0 0 2X 2X 2X 0 X X 0 0 0 X X 0 2X X 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 0 2X X 2X 2X 2X 2X X 2X 0 2X X X 2X 0 2X 0 0 0 0 2X 0 X 2X X X 0 X 2X 2X X X 2X X 0 2X X X X 2X 0 0 X X X 2X X X 0 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 0 X X X 0 X 2X 0 0 X 0 2X 2X 0 0 2X 0 2X X 0 X 2X 2X X 2X 2X 0 0 2X X 0 2X X 0 2X 0 2X X X X 2X X 0 X 0 X 0 0 X 2X 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 X X X 2X 0 0 2X 0 X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X X X 0 2X 0 2X 0 X 0 2X X X 2X 2X 0 0 2X 0 2X 2X 2X X 0 0 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X 2X 2X X 0 X X 0 2X 2X 2X X X 2X 0 0 2X 0 X X X 2X 0 2X 0 X 2X X X X X 2X 0 2X 2X X 0 X X 2X X 2X 0 0 X 0 2X X 0 2X 0 0
generates a code of length 71 over Z3[X]/(X^2) who´s minimum homogenous weight is 117.
Homogenous weight enumerator: w(x)=1x^0+36x^117+156x^120+12x^121+18x^122+286x^123+126x^124+174x^125+376x^126+462x^127+444x^128+420x^129+966x^130+1068x^131+486x^132+1794x^133+2088x^134+506x^135+2928x^136+3444x^137+584x^138+4080x^139+4614x^140+526x^141+4818x^142+5136x^143+586x^144+4530x^145+4416x^146+592x^147+3366x^148+2940x^149+486x^150+1974x^151+1344x^152+434x^153+828x^154+444x^155+382x^156+324x^157+108x^158+270x^159+36x^160+6x^161+210x^162+118x^165+50x^168+38x^171+14x^174+2x^177+2x^183
The gray image is a linear code over GF(3) with n=213, k=10 and d=117.
This code was found by Heurico 1.16 in 62.2 seconds.