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 1 0 0 1 1 2X 1 1 1 0 1 1 1 X 0 1 X 0 1 X 1 1 1 1 1 X 1 1 1 1 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 2X+1 1 1 X X 1 2 X 2X+1 1 X+1 2X X+2 1 1 1 1 1 2 0 2X+1 X+2 2X+2 X+2 2X 1 2 1 0 2X 1 0 2X+1 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 X 0 2X 0 0 X 2X X 2X X 0 2X 0 2X X 2X 0 2X 0 0 X X X X 0 2X 2X 0 X X 0 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 X X 0 X 0 X 0 2X X X X X 0 X X 2X X 0 0 X X 2X X 2X X 0 2X X X 0 2X X X 0 2X 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 0 2X 2X 0 2X 2X X 2X X 2X X 0 X X 0 X 0 2X X 2X X X X 2X 2X X 0 2X X X 2X 0 0 X 2X 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 0 0 X 2X X 2X 2X 0 0 X 0 X 2X 2X 0 2X X 0 X 0 2X 0 0 2X X X 0 X 2X 0 0 2X 0 2X 0 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 2X X 2X 0 2X X 0 2X 0 2X X X X 2X 2X X 0 0 2X X 0 0 X 2X X X X 0 0 0 0 X X X 2X 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 2X X X 0 0 X 0 2X X X 0 0 2X 2X X 2X 2X X 2X X 0 0 X 2X 0 0 0 2X 0 0 X 2X X 0 0
generates a code of length 61 over Z3[X]/(X^2) who´s minimum homogenous weight is 99.
Homogenous weight enumerator: w(x)=1x^0+58x^99+6x^101+204x^102+18x^103+90x^104+338x^105+138x^106+270x^107+438x^108+444x^109+786x^110+438x^111+1116x^112+1602x^113+524x^114+2640x^115+2862x^116+564x^117+4002x^118+4644x^119+554x^120+5328x^121+5292x^122+662x^123+5250x^124+4698x^125+622x^126+4308x^127+3342x^128+584x^129+2106x^130+1908x^131+508x^132+720x^133+594x^134+392x^135+156x^136+132x^137+270x^138+18x^139+18x^140+214x^141+108x^144+52x^147+22x^150+4x^153+4x^156
The gray image is a linear code over GF(3) with n=183, k=10 and d=99.
This code was found by Heurico 1.16 in 51 seconds.