The generator matrix
1 0 0 1 1 1 1 1 0 2X 1 1 1 1 1 1 0 X 1 0 1 2X 1 1 1 1 0 0 1 1 1 1 1 1 1 2X 2X X 1 1 1 X 2X 1 1 1 1 2X 1
0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2X+1 2X 2 0 1 2X+2 1 2X+2 1 1 0 1 2X 1 1 X+1 X+1 X+2 0 1 X+2 2X 2X 1 0 2X+2 X+1 0 1 1 2X 2X 2X+1 2X+2 1 0
0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 2X+2 X+1 X+2 1 2X 2X+1 2 0 1 1 X+2 2X+1 2X 2X 2X+1 2X X+2 2X 1 2X 2X+2 2X 1 2X 1 2X+1 0 X+1 2X+1 2X+2 0 2X+2 X 2 0 0
0 0 0 2X 0 0 0 0 0 0 0 0 0 2X 2X 2X X X X 2X 2X 2X 2X X 2X 0 2X 2X 0 X 2X 2X 2X 2X 2X 2X X 2X 0 X 0 2X 0 0 0 0 2X 2X 0
0 0 0 0 2X 0 0 0 0 0 X 2X 2X X 2X X 0 0 X 2X X X 2X X 2X X X 0 2X 0 X 2X 2X X 0 0 2X X 0 0 0 0 X 0 X X 2X X 0
0 0 0 0 0 X 0 X X 2X 2X 2X 2X 0 X X 2X 2X X X 2X 0 X 0 0 0 X 2X 0 0 0 2X 2X 2X X X 0 X 0 0 2X 2X 2X 2X X 0 0 0 0
0 0 0 0 0 0 X X X X X 2X X X 0 X 0 0 0 0 X 2X 2X 2X 0 2X 2X 0 2X 2X 2X X 2X 0 X 2X 0 2X 0 X 2X 2X X 0 2X 2X 2X 2X 2X
generates a code of length 49 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.
Homogenous weight enumerator: w(x)=1x^0+66x^81+18x^82+174x^83+418x^84+186x^85+696x^86+922x^87+642x^88+1650x^89+1598x^90+1218x^91+2784x^92+2436x^93+1968x^94+4566x^95+3510x^96+2712x^97+5682x^98+3778x^99+2946x^100+5268x^101+3380x^102+2112x^103+3378x^104+2140x^105+966x^106+1578x^107+896x^108+300x^109+360x^110+340x^111+54x^112+108x^113+120x^114+52x^117+14x^120+4x^123+8x^126
The gray image is a linear code over GF(3) with n=147, k=10 and d=81.
This code was found by Heurico 1.16 in 33.5 seconds.