The generator matrix 1 0 0 0 1 1 1 1 X 1 1 1 1 1 1 2X 1 1 X 1 X 1 0 1 1 1 0 1 1 1 2X X X 1 0 1 X 1 1 0 0 1 1 1 1 X 1 1 2X 2X 2X 1 1 1 1 1 1 1 1 1 1 1 0 0 1 X 1 1 X X 1 2X 1 1 1 0 1 1 1 2X 1 0 1 0 0 0 0 2X 2X 1 1 2X+1 X+2 2X+2 0 2X 2X 1 2 1 X+1 1 2X+2 1 2X+1 2 2X+1 1 X+2 2X+2 X+2 0 1 1 X 1 X+1 1 2X+2 1 1 1 X+1 X 2X+2 2X 0 1 X 1 0 1 2 X+2 2X+2 0 0 X 2 2X+1 2 2 X 1 2X X+1 1 2 2 1 1 2 1 X+1 1 2X+2 1 2X X X 2X 2X+1 0 0 1 0 0 0 2X+1 2 2X+1 1 2X 2X X+2 1 2X+2 1 2 X+1 X+2 X+1 X+1 2 0 2X+2 X X X 2X+2 1 X+1 1 1 2 1 2 X 2X 0 X+1 1 2 1 2 X 2X+1 1 2X+2 2X X+1 1 X 2 2X+2 2X+2 2X+1 1 X+2 X+2 X+1 2X+2 0 2 1 X 2X+2 X 1 2X 2X+2 2X+2 X+1 2X+2 2 X+2 X 2X+1 X+1 2X 2X 1 2X 0 0 0 1 1 2 2X+2 2 X+1 0 X+2 2X+2 2X+1 2X+1 X 2 X+1 0 2 X+2 2X 2 2X+1 0 0 2X 2 2X 2 1 2X+1 2 1 X X X+1 X+1 2X+1 X+2 X+2 2X+1 0 2 2 X+2 2X+2 2 0 2X 1 2 2X+2 1 0 0 0 X+1 X 0 X+1 X+1 X X 1 2X+2 2X+2 2X+1 2X 2 2X X X+1 2X 2X+1 2X+2 X+1 2X+1 X+2 X 0 2X+2 0 0 0 0 2X 0 2X 0 0 2X 2X 0 0 X X X X X 2X X X X X 0 2X 2X X X 2X 2X 0 2X 2X X 2X 0 X X 0 2X 0 2X X 0 X X X 2X 2X 2X 2X 0 X 0 2X 0 0 0 0 2X 0 X 0 X X 0 X 2X 0 0 X 2X 0 0 2X X X X 0 0 2X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X X 2X X 2X X X X X X X 2X X X X 2X 2X X X 2X 2X X X 2X 2X 2X X X 0 X 2X X X 2X 0 2X 0 0 2X 0 2X 0 2X 0 2X 2X 2X X X X X 2X X generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 145. Homogenous weight enumerator: w(x)=1x^0+246x^145+444x^146+212x^147+954x^148+1080x^149+386x^150+1698x^151+1974x^152+684x^153+2424x^154+2754x^155+692x^156+3300x^157+3330x^158+924x^159+3504x^160+3960x^161+900x^162+3966x^163+3984x^164+778x^165+3786x^166+3696x^167+824x^168+3120x^169+2580x^170+582x^171+1860x^172+1530x^173+326x^174+972x^175+696x^176+148x^177+318x^178+180x^179+40x^180+90x^181+36x^182+20x^183+6x^184+20x^186+6x^189+6x^192+10x^198+2x^204 The gray image is a linear code over GF(3) with n=243, k=10 and d=145. This code was found by Heurico 1.16 in 73.1 seconds.