The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 0 1 1 1 X 1 1 1 1 1 1 0 1 1 1 1 2X 1 1 1 X
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 1 2X+1 2 2X+1 1 2 X 2X+1 2X X X 1 1 X+1 2X+2 2X 1 2X+2 0 0 X
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 0 X 0 0 2X X 0 X 2X 0 2X 0 2X 2X X 0 X 0 X 2X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 2X X X 2X X 2X 0 X X 2X X X 0 0 0 0 2X 0 X X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X X 2X X X 0 0 0 0 0 2X
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 2X 0 X 0 2X 0 2X X X X 0 X 0 2X X X 0 2X X 2X
generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+194x^69+532x^72+928x^75+1268x^78+1622x^81+1136x^84+622x^87+174x^90+32x^93+20x^96+20x^99+10x^102+2x^105
The gray image is a linear code over GF(3) with n=120, k=8 and d=69.
This code was found by Heurico 1.16 in 0.44 seconds.