The generator matrix 1 0 0 1 1 1 1 1 1 1 1 0 2X 1 2X 1 X 1 1 1 1 1 X 1 1 2X 1 X 1 1 X 1 1 1 2X 1 2X 1 1 X 1 1 0 0 1 2X 0 1 1 0 1 X 1 1 1 1 1 0 1 1 1 1 1 1 2X 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 2 1 2X+1 2 2X+2 1 1 0 1 2X+2 1 2X+1 X 1 2X+1 2X 1 2X+2 2 2X X+1 1 2X+1 2 1 2X 0 2 1 2X+2 X 2X 1 2X X+2 X+2 1 0 2X 1 1 2X+2 2X+1 1 2X+1 1 X+1 X+1 2X+2 2X+1 0 1 X 2 2X X 2X+2 2 1 X 0 X+2 X+1 2X 2X+2 X+2 2 2X+2 0 X X 2X+1 0 0 1 1 2 2 2 1 2X 0 2X+1 2 2X+1 0 X+1 X+1 X+2 2X+2 X+2 2X+1 0 X+1 0 2X+2 2X 1 X+1 1 2X X 2X+2 X+2 2X+1 X+2 0 2X+1 1 2X+1 2 1 2 X X+1 1 0 0 0 X 2X X+2 X+2 2X+2 X+1 X X+1 1 0 X+2 X+1 2X X 2X 2X 2X+1 2X 2 X+1 X+1 X+2 X+1 2X+1 2X+2 X+1 1 X+2 2X 2X+1 2X+2 0 0 0 2X 0 0 0 0 0 2X 2X X 2X 2X X 0 2X 2X 2X X 2X 0 X X 2X 2X 2X X 2X 0 2X 2X X 0 0 0 X 2X 2X 2X 0 X 0 X 0 X X X 0 X X 2X 0 2X 0 X 0 0 2X 0 2X 0 X 0 2X 0 2X X X 0 X 0 2X 0 X 0 0 X 0 0 0 0 X 0 X 2X 2X 2X 2X 0 X X 2X X 2X 0 2X 0 X X 0 X 0 0 2X X 0 0 2X 0 0 2X X 2X 2X 2X 2X X X 0 2X 0 2X 0 X 2X 2X X 0 0 0 2X X 2X X 2X X 0 0 2X 0 0 0 0 0 X X 2X X 0 2X 0 X X 0 2X 0 0 0 0 0 2X X X 0 X 0 X X X 2X 2X 0 0 X X 2X X X 2X X 0 2X 2X 2X 2X 2X 2X 0 2X X 0 0 X 0 X 2X 0 2X 2X X 2X X 0 X 0 2X X X 0 X 0 2X 0 0 0 0 2X 2X X 2X 2X X X X 0 2X 2X X 0 X X 0 X generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 141. Homogenous weight enumerator: w(x)=1x^0+88x^141+204x^142+156x^143+368x^144+744x^145+390x^146+554x^147+840x^148+480x^149+882x^150+1158x^151+600x^152+960x^153+1146x^154+756x^155+978x^156+1410x^157+642x^158+980x^159+1170x^160+534x^161+736x^162+1002x^163+378x^164+534x^165+654x^166+282x^167+286x^168+264x^169+108x^170+114x^171+78x^172+42x^173+30x^174+66x^175+26x^177+12x^178+6x^179+8x^180+8x^183+6x^186+2x^192 The gray image is a linear code over GF(3) with n=234, k=9 and d=141. This code was found by Heurico 1.16 in 7.68 seconds.