The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 X 1 X 1 2X 2X 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 X 1 0 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 2X+1 1 2 0 2 1 2X+1 0 2 2X+1 X 1 X+2 2X+1 0 1 2X 1 2X+1 1 0 1 1 2X X+2 2X+2 X+2 2X+1 X 2X+1 2X+2 X+1 2X+1 1 X X 1 1 X+1 X+1 2 2X+1 2 X+2 X+2 2X 2X 1 0 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 X 2X X 0 2X 0 2X X 2X 0 0 X X 0 0 X 2X X X 2X 0 2X 0 2X 2X 2X 0 X X X 0 2X 0 0 0 2X 0 2X X X 2X 0 2X X X 0 2X 0 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X X X X 2X 0 X X 0 X 0 X X X 2X X 0 2X 2X X 2X 0 0 0 2X 2X 2X 0 2X X 2X 0 0 2X 2X 2X X 0 X 2X 2X 0 X X 0 X 2X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X X 2X 2X X 2X X 2X X X 2X 2X X 0 X X 2X X X 0 X 0 X 0 0 X 2X 2X 0 X 2X 2X 0 X 2X 0 X 2X X 2X 0 X 2X 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X X 2X 2X X 0 0 0 2X X 0 2X 0 X 0 2X 2X 2X 2X 2X 0 2X X X X X 0 X X X 2X X X 2X 0 2X 0 2X 0 X X 2X 0 2X 2X X X X 0 0 0 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X X X 0 0 X 0 2X 2X X 2X X 0 0 0 X 0 0 X X 2X 0 0 X 0 X 0 2X 0 0 2X 2X 2X X X X X 2X 0 2X 2X X 0 X X 0 0 X 2X 2X X 0 X
0 0 0 0 0 0 0 X X X X 0 2X X 2X 0 2X 2X 0 0 X 2X 2X 2X 0 X 2X 2X X 2X 2X 0 0 2X X X 2X X 0 0 0 X 0 2X 0 X X 0 0 X 0 0 2X 0 X 2X 2X 0 X X 2X X 0 0 X 2X 0
generates a code of length 67 over Z3[X]/(X^2) who´s minimum homogenous weight is 111.
Homogenous weight enumerator: w(x)=1x^0+74x^111+246x^114+30x^116+404x^117+72x^118+210x^119+910x^120+372x^121+306x^122+1610x^123+582x^124+864x^125+2406x^126+1212x^127+1596x^128+3944x^129+2034x^130+2118x^131+5362x^132+2550x^133+2568x^134+5946x^135+2580x^136+2280x^137+5374x^138+2034x^139+1866x^140+3020x^141+1074x^142+900x^143+1772x^144+510x^145+288x^146+908x^147+96x^148+84x^149+394x^150+6x^151+12x^152+222x^153+118x^156+56x^159+20x^162+12x^165+4x^168+2x^171
The gray image is a linear code over GF(3) with n=201, k=10 and d=111.
This code was found by Heurico 1.16 in 58.4 seconds.