The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 0 1 1 1 1 1 1 1 1 0 2X 1 0 1 1 1 1 1 1 1 X 2X 1 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 1 1 X+2 0 2X+1 1 2 2X+1 0 2 0 X+2 X 2X+1 1 1 2 1 X+1 2X+1 X+1 X 2X+1 X+1 2X+2 1 1 X 2X+2 2X+2 X+2 0 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 2X 2X X 2X X X X 0 2X 0 X 2X 0 X X X X X 0 0 2X X 0 2X X 2X 2X 2X 0 X 2X X 0 2X 2X 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 0 2X 2X X X 2X 2X X X 2X 0 2X X X 2X 0 2X 2X 2X 0 X X 0 X 2X 0 2X X 2X 0 2X X 2X X 0
0 0 0 0 X 0 0 0 X 2X 2X X 2X X 2X 0 2X X 0 X X 0 X 0 0 2X X 2X X 0 X X 2X X X 0 2X 2X 2X 0 X 0 X 0 2X X 2X 2X 0
0 0 0 0 0 2X 0 X 2X 2X 2X 0 X 0 2X X X X 2X 2X X X 0 2X 0 0 X 0 2X X X 2X 2X 2X 2X 2X 2X 2X 0 X X 0 0 0 X 0 0 2X X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X X X 0 2X 0 2X 0 2X 2X 2X 2X X 2X X 2X 2X 0 X 0 0 2X 0 2X 0 2X X 0 X X X 2X X 0 X 0 0
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+62x^81+6x^83+170x^84+42x^85+66x^86+510x^87+132x^88+240x^89+914x^90+372x^91+534x^92+1296x^93+690x^94+732x^95+2072x^96+1122x^97+1014x^98+2238x^99+930x^100+984x^101+1736x^102+780x^103+606x^104+1162x^105+258x^106+150x^107+420x^108+48x^109+42x^110+174x^111+82x^114+64x^117+26x^120+8x^123
The gray image is a linear code over GF(3) with n=147, k=9 and d=81.
This code was found by Heurico 1.16 in 4.73 seconds.