The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 1 0 1 1 0 1 1 1 1 X 1 1 1 1 X 1 1 1 1 2X 1 1 2X 1 1 1 1 1 1 1 1 1 1 1 1 2X 1 1 1 1 2X 1 1 1 X 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 2X+1 0 1 2 2X+1 1 2 X X+2 2X+1 1 2 X 2X X+1 1 X+1 2X+2 2X X+1 1 X+2 2X+2 1 1 X+1 X+1 2X+1 2 X+1 1 2X+1 X 1 X 1 1 2X 1 X+2 2X+1 1 0 2X+1 2X+1 1 0 X
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 2X X 0 2X 2X 2X X X X X 2X X 2X 0 0 0 2X 2X X 2X 2X 0 2X X 0 0 2X X 0 X 0 X 0 2X 2X 0 X 2X X 0 0 0 0 2X 2X 0 2X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 0 2X 2X 2X X X 2X 2X 2X X 2X X 0 X 2X 2X X 0 0 X 0 0 0 X 0 0 X 0 X X 2X X X 0 X 0 2X X X 2X 0 0 2X X X 0 2X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 X 0 0 X 2X 2X 0 0 X X 2X X 2X X 2X X X 2X 0 0 2X 0 0 2X 2X 0 X 2X X 2X 2X 2X X X 2X X 0 X 0 0 2X X 0 2X 2X X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 0 0 X 0 2X 2X X 0 0 0 2X 2X X X 0 2X 2X 2X 0 X X 0 2X 2X X 2X 0 0 0 2X X X 0 2X 2X X 2X X 2X X 2X X 0 2X X 2X X
generates a code of length 67 over Z3[X]/(X^2) who´s minimum homogenous weight is 121.
Homogenous weight enumerator: w(x)=1x^0+66x^121+196x^123+270x^124+278x^126+552x^127+192x^129+600x^130+472x^132+780x^133+342x^135+810x^136+222x^138+696x^139+278x^141+408x^142+90x^144+150x^145+18x^147+42x^148+36x^150+16x^153+38x^159+2x^162+4x^168+2x^177
The gray image is a linear code over GF(3) with n=201, k=8 and d=121.
This code was found by Heurico 1.16 in 2.79 seconds.