The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 1 0 1 1 1 1 1 2X 1 X 1 0 1 1 1 1 1 1 2X X 1 1 1 2X 1 1 1 1 1 1 0 X 1 1 1 1 0 X 1 1 2X 1 1 1 1 0 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 X+1 1 0 2 2X+1 X+1 2 1 2X+2 1 2X+2 1 0 2X+1 X 1 2X+2 X 1 1 2 2X+1 X 1 2X X+1 2X X+2 2X+2 1 1 1 2X+2 2X+2 2X+1 X 1 1 X+1 0 1 2X+1 2X+2 2X+2 1 X 2X+1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 0 X X 2X 0 X X X 0 2X 2X 2X X 0 0 X 0 0 X X X X 0 2X 0 0 X 2X 0 0 X 2X 2X 2X X 0 2X 0 X X 0 2X 0 X 2X 2X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 2X 2X 2X 2X X X X 2X 0 X 0 X 2X 2X X 2X X 2X 2X 2X 2X X X X 0 0 X X 0 0 0 0 X 2X X 2X 0 2X X 0 0 X 0 0 2X X 2X
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 X X 2X 0 X 0 2X 2X X X X 2X X 2X 2X X X 0 2X X X X 2X 2X 2X 2X X X X 0 2X 2X X 0 0 0 2X X X X X 2X X 0 2X 2X 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 X X 0 0 2X 0 X 2X 2X 2X 2X 0 2X 0 X 0 X 0 X 2X 0 X X 0 0 X X X 0 X 0 X X X X 2X 0 0 2X X X 0 X X X 0
generates a code of length 66 over Z3[X]/(X^2) who´s minimum homogenous weight is 120.
Homogenous weight enumerator: w(x)=1x^0+272x^120+596x^123+934x^126+916x^129+1090x^132+1102x^135+904x^138+478x^141+162x^144+38x^147+22x^150+14x^153+12x^156+8x^159+10x^162+2x^168
The gray image is a linear code over GF(3) with n=198, k=8 and d=120.
This code was found by Heurico 1.16 in 6.87 seconds.