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 2X 1 1 1 1 2X 1 1 1 X 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 2X 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 2X 1 1 1 0 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 1 X 2X+1 2 2X 1 X X+2 X+1 1 1 1 X+2 1 X+2 2 2X+2 1 X 1 2X 2X+2 2X 2X+2 X 2X+2 X X+1 2 X+1 2X 1 2X 2X+2 2X X+2 2X+2 1 2 2 2X 2 1 2X+2 2 1 2X+1 X 1 X 1 X+2 2X+2 2X+1 1 X+2 0 2
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 2X X X X X 2X X 2X 2X X 0 X X 0 X 0 X X X 2X 0 0 0 X 0 X 0 0 0 X 0 2X X X 2X 0 2X X 0 X 2X X X 0 2X 2X 2X 0 0 0 2X 0 X X X 0 X 0 2X 2X X 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 0 2X 2X 0 X 2X 0 2X 0 2X 2X 2X 2X X X 2X 2X 2X 2X 2X 0 2X X X 0 X 0 2X X X X 0 X 2X 2X 2X 0 0 X 2X 0 0 0 0 0 0 X X 0 2X X 2X 2X X X 0 X X 0 2X 0 2X 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 X 0 2X 2X 0 2X 2X X 2X X 2X 0 X 2X 0 2X X 2X X 2X X 0 0 X 2X 2X 0 2X X 0 0 2X 2X X 0 2X 2X X X X 0 2X X 0 X 2X X X 2X 2X 2X 2X X 0 2X 0 2X 2X X 2X 2X 0
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 0 0 2X 0 X 2X X 2X X 0 0 X 0 2X 2X 0 0 2X X X 2X 2X X 0 X 2X X 2X X 0 X 0 0 2X 2X 0 0 X X 2X X 0 0 X X 0 0 X 2X 2X 0 2X X 0 2X X X 2X X 2X X 0
generates a code of length 82 over Z3[X]/(X^2) who´s minimum homogenous weight is 150.
Homogenous weight enumerator: w(x)=1x^0+62x^150+6x^151+60x^152+300x^153+120x^154+186x^155+416x^156+162x^157+156x^158+542x^159+222x^160+162x^161+462x^162+246x^163+270x^164+578x^165+270x^166+258x^167+482x^168+240x^169+192x^170+352x^171+120x^172+84x^173+220x^174+54x^175+72x^176+98x^177+18x^178+18x^179+48x^180+32x^183+8x^186+8x^189+14x^192+14x^195+8x^198
The gray image is a linear code over GF(3) with n=246, k=8 and d=150.
This code was found by Heurico 1.16 in 1 seconds.