The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 0 1 1 2X 1 1 1 1 0 1 X 1 1 1 1 1 1 1 1 1 0 X 2X 1 1 X 1 1 1 1 0 2X 1 1 1 1 X 0 1 1 1 1 1 1 1 1 0 1 1 1 X 1 1 X 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 X+1 0 2 1 X 2X+1 1 2 2 2X+1 0 1 0 1 2X+2 1 X 2X+2 X+1 2X+2 2X+1 X 1 1 1 1 2X X+2 1 2X+1 X X+1 2X 1 1 X+2 0 2X+2 X 1 1 2X X 2X+1 2X+2 2 2X+2 2 2X+2 1 X X 0 1 2X+1 2X 1 2 0 X+2 2X+1 2 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X 0 X 2X 2X X 2X 2X 2X 2X 0 2X 2X 0 X X 2X 0 2X X 2X 2X X 2X 2X X 0 X 0 0 2X X 0 2X 2X 2X X X 0 2X 2X X X 2X 2X X 0 2X 0 0 2X 0 0 2X X 2X 0 0 X X X 2X 0 X 0
0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X X 2X 0 2X 0 0 X 0 2X 2X 2X X X X 2X 0 X 2X 0 2X X X 0 X 2X 2X 2X X 2X X X X 2X 2X 0 2X 0 2X 2X X X 0 X X 2X 0 0 X X X X X 0 0 0 2X 0 X X X 0 2X 0 0
0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X 0 2X 2X X 2X X X X 2X 0 0 2X 2X 0 0 0 2X X X X 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X X X 0 X 0 2X X 0 X 0 X X X X 2X 2X X X 0 0 X 2X 2X 2X X 0 0 2X 0 X X 2X 0 X
0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 0 X X X X 2X 0 X 2X 0 X 0 2X 2X X X 2X 0 0 2X X X 0 2X 0 X 0 0 0 2X X 2X X X 2X 2X X 0 0 0 0 X 2X X 2X 2X 2X X 0 X 0 0 0 X 0 X X X X 0 2X 0 0 0 2X
0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X X 2X X 0 X X 2X X X X X 0 0 X X 0 2X X 0 X 0 X X 0 0 0 2X X X 0 0 0 X 0 0 X 2X 0 X 2X 0 X 2X 2X 0 X X 2X 0 2X X 0 0 X 0 2X 2X X 0 0 0 X X 0 2X
generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 147.
Homogenous weight enumerator: w(x)=1x^0+62x^147+42x^148+12x^149+186x^150+96x^151+132x^152+456x^153+186x^154+240x^155+814x^156+414x^157+414x^158+1066x^159+516x^160+516x^161+1450x^162+498x^163+654x^164+1740x^165+726x^166+774x^167+1704x^168+630x^169+696x^170+1514x^171+552x^172+528x^173+1020x^174+432x^175+258x^176+446x^177+210x^178+114x^179+142x^180+60x^181+36x^182+100x^183+6x^184+86x^186+6x^187+62x^189+38x^192+18x^195+20x^198+6x^201+4x^204
The gray image is a linear code over GF(3) with n=249, k=9 and d=147.
This code was found by Heurico 1.16 in 9.54 seconds.