The generator matrix 1 0 0 0 1 1 1 1 1 1 2X 1 1 1 X 1 X 1 X 1 1 1 0 1 1 2X 2X 1 1 1 1 1 0 X 1 X 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 X 1 0 1 2X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 0 0 1 1 1 0 1 0 0 0 0 2X+1 1 2X+2 2X+1 1 1 X 2X 1 2X+1 1 1 0 X 2 2 1 2 2 1 1 2X+2 X+2 1 2X 2X+2 2X 1 2X 1 2X+1 0 2X+1 1 2X X+1 X X 2X 1 X+2 1 1 1 1 2X+2 0 X+2 2 1 0 0 X 1 0 2 0 2X+2 X 1 X+2 2X 0 2X 1 2X+2 2X 0 2X 1 2X+2 2X+2 2X 0 0 1 0 1 0 2X 2 2X+1 X+2 2X+2 1 2 X+2 2 2X 0 2X+1 1 2X+2 2X+1 X 2X+2 X+2 X+2 2X 1 X 2X 0 2X+1 2X+1 1 2X+1 0 2X+1 X+2 2X+2 2X+1 X+2 X+1 X+1 X+1 2X X 2X 2X+1 X+1 2X+1 2X+2 X+2 X+1 2X X+2 2X 2 1 1 1 X+2 X+1 2X+2 2X+1 1 0 0 2X+2 2X 2X+1 1 2X+1 2X+2 X 2X 1 2X+1 X X 0 0 0 0 1 2 1 2X+2 2X+1 X 0 2X+1 X+2 2 X 2X+2 0 X+1 1 1 2X+1 X+1 2X+2 2X X 2 2X+2 2X 2X 2X+1 1 2X X+2 X+2 2X+2 2X+2 X+1 X+2 1 X+1 X+1 2X+2 0 2X+1 2X+1 X 2X 0 2X X 2 0 2X+1 0 X+1 0 1 2X 1 2X 1 2X+1 2X+1 2X+1 2 X+2 X X X+2 1 1 2X X+2 2X+1 1 0 X 1 2X X+1 0 0 0 0 2X 0 2X 0 X X 0 X X 0 2X 0 X 2X X 2X 0 X X 2X 0 X 0 X 0 X 2X 0 0 2X 2X 0 0 2X X X 2X 2X X 2X 0 0 X 0 0 X 2X 0 X 0 2X X 0 2X 2X 2X 0 2X X 0 0 2X X 2X 2X 0 X X 2X 0 X 0 2X X 2X 0 0 0 0 0 2X 0 2X X X 0 X X 2X X 2X 2X 0 2X 0 2X X 2X 2X X X 2X 2X 0 0 X X X 2X 2X X 0 2X 2X 2X X 2X 2X X X X 0 X X 0 2X 0 X X X 2X 2X 2X 2X 0 X X 0 0 X X X X X 2X X 2X 2X 0 2X 2X X 0 2X generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 141. Homogenous weight enumerator: w(x)=1x^0+194x^141+342x^142+270x^143+674x^144+1242x^145+816x^146+1352x^147+1962x^148+1080x^149+1838x^150+2766x^151+1446x^152+2326x^153+3342x^154+1896x^155+2654x^156+3954x^157+1896x^158+3138x^159+3894x^160+1968x^161+2806x^162+3510x^163+1656x^164+2266x^165+2838x^166+1296x^167+1442x^168+1518x^169+576x^170+606x^171+594x^172+168x^173+276x^174+264x^175+48x^176+62x^177+12x^178+6x^179+16x^180+6x^181+14x^183+4x^186+6x^189+6x^192+2x^201 The gray image is a linear code over GF(3) with n=237, k=10 and d=141. This code was found by Heurico 1.16 in 64.1 seconds.