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 1 1 X 1 1 1 0 1 1 1 1 1 1 1 2X 1 1 1 2X 0 1 2X 1 1 0 1 1 2X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 2X+1 2 2 X 1 X+1 2X X 1 2X+1 2X X+2 2X 2X+1 2 2X+2 1 X+1 0 2X+2 1 1 X 1 0 X 1 X 2X+2 1 2 0 2X+1 1 X+1 1 2X+2 X X 2X 2 2X+2 X+2 1 0 2X 2X+1 0 2X+1
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 2X X X 0 X 2X 0 2X X X 2X 0 X 0 0 2X 0 2X X 0 X X 0 2X 0 X 2X X 2X 2X X X X 2X 2X X 2X 2X 0 2X 2X X 0 0 2X 0 X X X X X
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 0 2X 2X 0 2X X 0 X X 0 0 X 2X X 2X X X 2X X 2X 0 2X 0 0 2X X 0 X X X X 0 2X X X 2X 2X 0 2X 0 0 2X 0 2X X 0 0 X 2X X X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 X 0 2X 0 2X 2X 2X X X X 2X X X 2X 2X X 2X 0 X X 0 2X 0 X 0 2X 2X 0 0 2X X 2X X 0 0 X X 0 0 X 2X 0 0 X 2X 2X X 0 X 0 0
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 0 0 2X X 0 2X 2X 0 0 2X 2X X 2X 0 X 2X 2X X 0 0 X 2X X X 2X 2X X X X 0 X X 0 0 2X 2X 0 0 0 2X 0 2X 2X 0 0 2X 0 2X 2X 0 X
generates a code of length 71 over Z3[X]/(X^2) who´s minimum homogenous weight is 129.
Homogenous weight enumerator: w(x)=1x^0+130x^129+544x^132+806x^135+902x^138+1070x^141+1166x^144+866x^147+706x^150+220x^153+70x^156+22x^159+18x^162+6x^165+12x^168+10x^171+6x^174+4x^177+2x^180
The gray image is a linear code over GF(3) with n=213, k=8 and d=129.
This code was found by Heurico 1.16 in 0.882 seconds.