The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 0 1 1 1 1 0 1 1 2X 1 2X 1 1 1 1 0 1 1 1 1 2X 1 1 1 1 1 1 1 1 1 X 1 1 0 1 1 1 2X 0 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 2X 1 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 2 1 1 2X+1 2 0 X+2 1 0 2X+1 2 X+1 1 X+2 X 1 2X+1 1 0 X+2 2X 2X+1 1 2X+2 1 X 2X 1 2X+2 2X+1 2X X+2 1 2X+2 X+2 2X 2X+1 1 X 0 1 2X+2 X+1 0 1 1 0 2X+2 2 2X+1 2X X+1 2 2X+2 X 2 1 2X 2 2X+2 X+1 1 2X+1 0 0 0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X 2X X 2X 2X X 2X X X 0 2X 0 2X 2X 2X 2X 0 2X 0 0 0 2X 2X X X X 0 X 2X X 0 2X 2X 2X 2X X 2X 0 X X 2X 2X 2X X 0 X 2X X 2X X 2X X X X X X 0 2X 0 2X 0 2X 0 0 0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X 2X X 0 2X 2X 2X X 2X 0 2X 0 X 2X X 0 2X X 0 X X X 0 2X 2X 2X 0 X X 2X 2X X 0 2X 2X 2X 2X X 0 0 0 2X X X 2X X 0 X X 2X X 0 0 2X 2X X 0 0 0 X X 2X 2X X 0 0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X X 0 0 X 2X 2X 0 0 X X 2X X X 0 2X 2X 0 2X X 0 2X 2X X X X X 0 2X 0 X 2X 2X 2X X X X 0 0 2X 2X 2X 2X 0 X X X X X 0 X 2X 2X 2X 2X 2X 2X 0 2X X X 2X 2X 2X X 0 0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X X 0 2X X 2X X X X X 0 0 2X 2X X 2X 0 2X 0 X 0 X 0 X 0 X 0 X 2X X X 0 X 0 0 0 X 0 X 0 X 0 2X X 2X 0 2X 2X 2X 0 0 0 2X 2X X X 2X 2X 0 X X X 2X X 0 0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X 0 2X X X 0 0 0 X 2X 2X 2X 0 X X 0 0 0 2X X 2X X X X X 0 X X 2X 2X 0 0 0 X 0 X 2X X 0 2X X X 2X X 2X X 2X 0 0 0 0 0 0 2X 2X 2X 0 0 X X 0 2X X 0 0 0 generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 138. Homogenous weight enumerator: w(x)=1x^0+56x^138+174x^141+24x^142+54x^143+408x^144+84x^145+150x^146+716x^147+252x^148+318x^149+1022x^150+468x^151+498x^152+1292x^153+624x^154+702x^155+1534x^156+702x^157+750x^158+1550x^159+972x^160+840x^161+1564x^162+678x^163+648x^164+1200x^165+432x^166+282x^167+694x^168+102x^169+120x^170+356x^171+18x^172+12x^173+114x^174+18x^175+90x^177+64x^180+48x^183+30x^186+10x^189+2x^192+4x^195+4x^198+2x^201 The gray image is a linear code over GF(3) with n=237, k=9 and d=138. This code was found by Heurico 1.16 in 8.83 seconds.