The generator matrix 1 0 0 0 0 1 1 1 2X 0 2X 2X X X 1 1 1 X 1 X 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 2X 1 1 1 1 1 X 1 1 2X 1 X 1 1 1 2X 1 2X 1 1 1 1 0 1 1 1 X 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 2X X X+2 X X+2 2X 2X 2 2 2 X+2 2X 1 1 2X+1 2X 1 2X+2 1 X+1 2X 1 1 X X+1 2 2X+1 2X X+1 1 X 2X 1 X+1 X+2 1 2X 2X 0 X+2 X+1 1 2X+2 1 X+1 X+2 X+2 X 1 X 1 2X+1 2X X+2 2X 2X+1 X 2X+2 1 X+2 1 X+2 2X+1 0 0 1 0 0 0 1 2X+1 1 1 2X 2X+1 2X+2 2X+2 2 2 X+1 1 2X 1 1 1 X 2X 2X+1 2X+2 2X+2 X+1 0 2X+1 2X 2 1 0 2 X+2 X+1 2X+1 1 2X 0 1 X X+2 2X+1 2X+2 X+2 2 X+1 2X 1 0 2X 2X 2 X+2 X+2 2X+1 2X+2 2 2X+2 1 X 1 2X+1 1 2X+2 2 1 2X+1 X+2 2 X 1 1 1 2 0 0 0 1 0 1 1 2X+2 X+1 X+1 2X+1 X+2 X 2X+2 0 2X+2 X+1 1 0 X+2 X X+2 1 2X+2 2X 2X+2 X 2X+1 2X 1 2X+2 0 X+2 2X+1 X 2X+1 X+1 0 2X+2 X 2X+2 2X+1 2X+2 X+2 2 2X+2 2X+2 X 2X 2X+1 X X+1 1 0 X+1 2X+1 X+2 2X+1 0 X+2 2 2X+2 2X+1 2X 1 X+1 X+1 X+1 2X X+1 2X+1 2X 0 2X+1 X 2X+2 0 0 0 0 0 1 2 X 2X+2 2 X X+2 2 2X+2 0 2 X 2 1 1 2X+1 X+2 X 2X 2X 0 2X+1 1 0 2X X+2 X+1 0 0 X+2 X+1 2X+2 2X+1 1 X+2 2X+2 0 2X 2 2 0 2X+2 1 X+1 1 2X+1 1 1 X+2 2X+1 2 X+1 X+2 2 0 2X 1 2 2X 1 X 2X+2 2 1 X+2 2X+1 2X+2 1 X+2 2X+2 X+2 2X+2 X+1 0 0 0 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 0 0 0 0 2X X 2X 2X X 0 2X 0 2X 2X X 2X X 0 X X 0 2X 2X 0 X 0 X 2X 0 X X X 2X 2X X 0 X X 2X X 0 0 2X X 0 X 2X 0 0 X 0 0 X 2X 2X 2X 0 X 2X 0 0 2X generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 135. Homogenous weight enumerator: w(x)=1x^0+476x^135+276x^136+564x^137+1724x^138+972x^139+1110x^140+3922x^141+1980x^142+2250x^143+6474x^144+3102x^145+3582x^146+9606x^147+4092x^148+4896x^149+12932x^150+5454x^151+5646x^152+15540x^153+6192x^154+6414x^155+15748x^156+6432x^157+5832x^158+13628x^159+5286x^160+4644x^161+9482x^162+3018x^163+2610x^164+5598x^165+1716x^166+1248x^167+2312x^168+660x^169+414x^170+716x^171+156x^172+114x^173+202x^174+18x^175+36x^176+34x^177+12x^178+6x^179+8x^180+6x^183+4x^186+2x^192 The gray image is a linear code over GF(3) with n=231, k=11 and d=135. This code was found by Heurico 1.16 in 590 seconds.