The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 X 1 1 1 1 1 0 2X 1 1 1 1 1 1 0 1 1 1 2X 1 1 1 0 1 1 1 2X 1 1 2X 2X 1 1 1 1 1 1 2X 1 X 1 1 1 1 2X X 1 1 2X 1 1 1 1 1 X 1 1 1 1 1 0 1 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 0 1 2X+1 2 2X+2 X+1 X 1 1 0 2X+1 2 X 2 1 1 2 2X 2X+1 1 X+2 2X 1 1 1 0 1 1 2 2X+2 1 1 2X+2 2X+1 X X+2 2X+2 2X+1 1 X+2 1 2X 2X+1 X X+1 1 1 X+1 0 1 X+2 X+1 2 1 X+1 1 2X+1 X+1 0 2X X+1 X 2X+1 0 0 0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 2X X 2X X X X X 2X 2X 2X 2X 0 2X 0 X X X X X X 2X 0 2X 2X X 0 2X X 2X 2X X 0 2X 2X X 2X X 0 2X 2X X 0 2X 0 X 0 X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 0 2X 2X 2X X X 0 X 0 X 2X X 0 2X X X 2X X X 0 X 2X 0 2X 0 2X 0 X X X 0 X 0 X X X 0 X X 2X 2X X X X 0 0 0 X 0 0 X 0 X X 2X 2X 2X 2X 2X 0 0 2X X X 2X 0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X X X 2X X 2X 0 X 2X 0 2X X 2X X 2X X 0 2X X X 0 0 2X X 0 0 2X 0 X 2X 0 0 2X 2X 0 X 2X 2X 0 2X X X 0 2X 2X 0 0 2X X 2X 0 X X X 2X X X 2X 2X 0 X 2X 0 2X 0 2X 2X 0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 0 0 X 2X 2X 0 2X 2X 0 0 0 X 2X 0 X 0 2X X 0 X X X 2X 0 2X X 2X X 0 2X 0 2X 0 X 0 X 0 X X 0 2X 0 2X X 2X X 2X 2X X 2X X 2X X 0 0 0 X 0 2X 0 0 0 2X 0 0 X 0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 0 X 2X 0 X 0 2X 0 X X X X X 0 X X 0 X 2X 0 X X X X 0 X 0 2X 0 2X X X 0 0 2X 0 2X 2X 2X 0 X X X 0 2X X 2X 2X 0 2X 0 0 2X 0 X X 0 2X 2X 2X 0 2X 2X 2X 0 X generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 144. Homogenous weight enumerator: w(x)=1x^0+110x^144+30x^145+66x^146+188x^147+186x^148+252x^149+226x^150+540x^151+522x^152+202x^153+834x^154+1032x^155+176x^156+1062x^157+1182x^158+182x^159+1368x^160+1368x^161+220x^162+1518x^163+1590x^164+150x^165+1350x^166+1380x^167+142x^168+990x^169+846x^170+126x^171+570x^172+390x^173+98x^174+210x^175+102x^176+96x^177+72x^178+18x^179+96x^180+18x^181+68x^183+44x^186+26x^189+22x^192+12x^195+2x^198 The gray image is a linear code over GF(3) with n=243, k=9 and d=144. This code was found by Heurico 1.16 in 9.39 seconds.