The generator matrix 1 0 0 1 1 1 1 1 1 1 1 0 2X 1 2X 1 X 1 1 1 1 1 1 0 0 1 2X 1 1 1 1 1 1 2X 1 0 0 1 1 1 1 1 0 2X 1 1 1 0 1 1 1 1 2X 1 X 1 2X 1 1 0 1 1 1 1 1 1 1 1 1 1 1 2X 0 1 1 X 2X 1 X 1 X 1 X 1 1 1 0 1 0 0 0 1 2 1 2X+1 2 2X+2 1 1 0 1 2X+2 1 2X+1 X 1 2X+1 2X 2X+2 0 1 2X+2 1 2 2X 2 2X 2X+1 1 1 2 X 1 2X+1 X X+1 2X+2 2 1 0 0 2 2X+2 1 2X X X+2 2X 1 2X+1 1 1 2X 1 2 1 2X 2X 2 2 0 1 X+1 X+2 2 2X+2 2X+1 1 1 X X+1 1 1 0 1 2X+2 1 2X+2 1 X X 0 0 0 1 1 2 2 2 1 2X 0 2X+1 2 2X+1 0 X+1 X+1 X+2 2X+2 X+2 2X+1 0 X+1 2X 1 0 2X+2 2X X+1 2X+2 2X+2 2X 2X 2X+2 2X+1 2X+2 1 2X 1 1 0 1 2X 2X+2 1 2X+1 0 X+1 2X+1 0 X+1 X+2 2X+2 X+1 X+1 0 X+1 1 2X 2 2 2X+1 2 1 X+2 X+2 X 2X 2X+1 2 2X+2 2 2 X 2X+2 X+2 2X 0 2X+1 2X+1 0 2X 2X+2 X+1 X+1 X 0 0 0 0 2X 0 0 0 0 0 2X 2X X 2X 2X X 0 2X 2X 2X X 2X 0 X 2X 2X 2X 0 2X 2X 0 X X X X 0 2X 2X X X 0 2X 2X 2X 2X 0 X 2X 0 2X 2X 0 0 0 0 X X 0 0 2X 0 X X 0 X 2X 2X X X X 2X 0 2X 0 2X 2X 0 2X X X 2X X X 0 0 0 X 0 0 0 0 X 0 X 2X 2X 2X 2X 0 X X 2X X 2X 0 2X 0 X X X 2X 2X 0 X X X 2X 0 2X 2X 2X 0 X 0 X 0 X 0 0 2X X 2X 0 2X 2X 0 2X 2X 2X 2X 0 X X 2X 0 2X 0 X 2X 2X 0 0 2X X 2X X X X X 2X 2X 2X 2X 2X X X 2X 0 2X 0 2X X 2X 0 0 0 0 0 2X X X 0 X 0 X X X 2X 2X 0 0 X X 2X X 0 X 2X X X 2X 0 0 0 2X 0 X X X 0 X X 0 2X X X 2X X 2X X 0 2X 2X X 2X 2X 0 0 2X X X 2X 2X X X 2X X X 2X 2X X 2X X 2X X X X 2X 2X X 0 X 2X 2X X 2X X X 0 generates a code of length 86 over Z3[X]/(X^2) who´s minimum homogenous weight is 156. Homogenous weight enumerator: w(x)=1x^0+50x^156+72x^157+192x^158+390x^159+336x^160+594x^161+606x^162+420x^163+1008x^164+694x^165+492x^166+1140x^167+784x^168+528x^169+1362x^170+928x^171+708x^172+1320x^173+946x^174+552x^175+1050x^176+776x^177+498x^178+936x^179+648x^180+354x^181+696x^182+436x^183+270x^184+252x^185+156x^186+96x^187+132x^188+64x^189+30x^190+54x^191+42x^192+18x^193+12x^194+10x^195+10x^198+6x^201+6x^204+2x^207+4x^210+2x^213 The gray image is a linear code over GF(3) with n=258, k=9 and d=156. This code was found by Heurico 1.16 in 8.63 seconds.