The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X 1 1 1 1 1 1 X 1 1 1
0 X 0 0 0 0 0 0 0 0 X X X 0 X X 0 X 2X 0 X 2X X 2X 2X 2X 2X 0 0 X X 0 2X 0 X 2X X X X X 0 X 0
0 0 X 0 0 0 0 0 X X 2X 2X 2X 0 X X X 0 0 2X X X 0 0 X 2X 2X 0 X 2X X X 0 0 2X 0 X X 2X 0 0 X 0
0 0 0 X 0 0 0 X 2X 2X 2X X X 0 0 X X 2X X 0 2X X X 0 0 0 2X X 2X 2X 2X X X 0 X 2X X X 0 X 2X 2X 0
0 0 0 0 X 0 0 2X 2X X X 0 2X X 0 0 X X 0 2X 0 X 0 2X 2X X X X 0 2X X 2X 0 X X 0 X X 0 2X X 0 0
0 0 0 0 0 X 0 2X X 2X X 2X 0 X X 2X 0 0 2X 2X 0 2X 0 X 2X 2X 0 0 2X 2X 0 2X 2X 0 2X 2X 0 X 0 2X 0 X X
0 0 0 0 0 0 X X 0 X 0 X 0 X 2X 0 2X X 2X X 2X 2X X 0 X 0 2X X 0 2X X 2X 0 2X 2X X 0 X 2X 2X 0 0 2X
generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+46x^69+140x^72+182x^75+404x^78+884x^81+1376x^84+1520x^87+1020x^90+532x^93+202x^96+130x^99+68x^102+42x^105+12x^108+2x^111
The gray image is a linear code over GF(3) with n=129, k=8 and d=69.
This code was found by Heurico 1.16 in 0.715 seconds.