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 1 X 1 X 1 1 1 1 X 1 1 X 1 X 1 1 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 X X 2X 2X 2X X 2X X X X 2X 2X 0 2X 0 X 0 X X 0 0 X 0 2X 2X X 0 X X X 0 2X 0
0 0 X 0 0 0 0 0 0 0 0 X X 2X X 0 X 2X 2X 2X 0 0 X X 2X X X 2X 2X X 2X 0 X 0 X X 2X X X 2X X 2X 2X 2X 2X 0
0 0 0 X 0 0 0 0 X 2X 2X 2X 2X 2X X 0 X 2X 0 0 0 2X 2X X 0 2X X 0 X 2X 2X 0 0 2X 2X X X 2X 0 2X 2X 2X 0 X 2X 0
0 0 0 0 X 0 0 X 2X 0 2X 2X X X X 2X X X 0 2X X 2X 2X 2X X 0 2X X X 2X 2X 2X 0 X X X 0 0 X 2X X X 0 2X X 0
0 0 0 0 0 X 0 2X 2X X 0 2X 2X X 2X 2X X 2X 2X X 2X X 2X 2X 0 X X 2X X X 2X 2X 2X 0 X 2X 0 2X X 0 X 0 2X 0 0 X
0 0 0 0 0 0 X 2X 2X 2X 2X X 0 X X 0 0 X 2X X X X X 0 2X 2X 0 X 0 0 2X 2X 0 2X 2X 2X 0 X 2X 0 0 2X 0 X 2X 2X
generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 75.
Homogenous weight enumerator: w(x)=1x^0+50x^75+118x^78+238x^81+18x^82+246x^84+180x^85+218x^87+720x^88+228x^90+1440x^91+208x^93+1440x^94+206x^96+576x^97+226x^99+158x^102+138x^105+86x^108+40x^111+20x^114+4x^117+2x^123
The gray image is a linear code over GF(3) with n=138, k=8 and d=75.
This code was found by Heurico 1.16 in 0.792 seconds.