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 X 1 1 1 1 1 2X 2X X 1 1 1 1 1 X 0 0 1 2X 1 1 2X 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 X 1 1 1 1 1 X 2X 1 1 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 2 2X+1 1 2X+1 2 X+1 X 2 X 1 1 2 2X+2 X+2 2X+1 0 1 1 1 2X+2 0 2X+1 2X 1 1 X+1 2X+2 X 0 1 2X 2X+2 2X 2X+2 1 2X+1 1 X 2 2X X+1 X+2 1 1 1 1 X+1 0 X 2X 1 1 X+2 2X+2 2X+2 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 X 2 0 2X+2 X+1 X+1 2 X+2 1 X+2 2 1 X 2 X+1 0 1 X 2X 2X 1 2X+2 X+2 2X+2 X 2X+1 1 X X 2 1 2X+1 X+1 X+2 1 0 2 X 2X+2 0 0 X X+2 2X 2X+1 1 2X+1 X+2 X+1 X+2 2X 2X 0 0 X 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 X 2X+2 X+2 1 X+1 X+1 2X X+1 2X X+1 2X+2 X+1 1 0 X 2X+2 2X+1 2X+1 1 2X X+1 2X+1 0 X 2X 2X+2 1 1 0 X+1 X X+1 X 1 2X+1 2X+2 X+2 2X+2 0 1 2X+2 2 X X+1 2X 1 0 X 2X+2 2X+1 2X X 2 2X 0 0 0 0 2X 0 2X 0 0 2X 2X 0 0 X X X X X 2X X X X X 2X 0 0 2X 2X 0 X X 0 X 2X 2X 2X 2X X X 0 2X 2X 0 0 X 2X 0 0 2X X 0 2X 0 2X 2X X 0 2X X 2X 2X 2X 2X 0 X X X X 0 0 0 2X 2X 2X X 0 X 2X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 2X X 2X 2X 2X X X X 2X X X X 2X X X 2X 2X X 2X 2X X X 0 X X X 2X 2X 2X 2X 0 X X 0 0 0 X X 0 X 2X X X 2X 2X 0 0 X 2X 2X generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 139. Homogenous weight enumerator: w(x)=1x^0+144x^139+282x^140+420x^141+786x^142+978x^143+906x^144+1308x^145+1674x^146+1228x^147+2094x^148+2220x^149+1808x^150+2670x^151+2874x^152+2000x^153+3210x^154+3234x^155+2208x^156+3396x^157+3252x^158+2458x^159+3042x^160+3090x^161+2058x^162+2610x^163+2436x^164+1094x^165+1554x^166+1182x^167+700x^168+738x^169+450x^170+306x^171+216x^172+162x^173+64x^174+102x^175+30x^176+22x^177+6x^179+10x^180+8x^183+8x^186+2x^189+6x^192+2x^195 The gray image is a linear code over GF(3) with n=234, k=10 and d=139. This code was found by Heurico 1.16 in 62.6 seconds.