The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 0 1 1 1 1 0 1 1 1 1 2X 1 1 1 1 1 0 2X 1 1 2X 2X 1 1 1 1 1 1 0 1 X 1 1 1 1 1 1 X 1 1 1 X 1 1 1 1 2X 0 2X 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 2 0 1 2 1 0 2X+1 2 1 0 X+1 X+2 1 1 0 2X+1 2 1 0 2X+2 2X+1 X 1 2X+1 2 X 2 1 X+1 2 X 1 2X+1 1 1 2X+1 X+2 1 1 X+2 0 2X 2X+2 2X 2 1 X+1 1 0 X+2 2X+2 2X+1 X X+2 1 X+1 X+1 X+1 1 2X+2 0 2X+1 2X 1 1 1 2X+1 2X+1 2X+1 X X+1 0 1 2X 2X+1 2X+2 X+2 2 0 0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X X 0 X 2X X 2X 2X X 0 X 0 2X 2X 2X 0 2X X X 0 2X X 0 0 X 2X 0 X X 2X X 2X 2X X 0 0 0 X 2X 2X X X X 0 0 X 2X 2X X 2X X X 2X 0 2X 0 2X 0 2X 0 X 0 2X 0 0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X 2X 2X X X X X 0 2X X X X 0 X 2X 2X 0 2X X 2X 2X X X X X 0 X 2X 0 X 0 X X 2X X X 0 0 0 0 X 2X 0 X X 2X X X X X 0 2X 0 X 0 0 0 2X X 0 2X X 0 0 0 0 0 0 X 0 0 0 X 2X 2X 0 X 2X 2X 0 0 2X 0 X X 2X X 0 0 0 X 2X X 2X 0 0 X 2X 2X 0 X 0 0 2X 2X 2X 2X X X 0 2X 2X X X 2X X X 0 0 2X X 0 2X 0 X X 2X X X 2X X 0 X X X 0 0 2X 0 0 X X 2X 2X 0 0 0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 0 0 X 0 2X X X 0 0 0 X 2X 2X 2X 2X 2X X 2X 2X X 0 2X X 2X 2X 0 2X 2X 2X 0 2X 0 X 0 0 X 0 2X 2X X X X X 0 X X 0 2X X X 0 2X 0 X 0 0 0 0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 2X 2X X 2X 2X 0 X X 0 2X 0 0 0 2X 2X X 0 2X X X 2X 0 X 0 X 2X 2X 0 0 X X 0 2X 2X 0 2X X 2X X 2X 2X X 2X 2X X 0 X 2X 2X 0 2X 0 0 X 2X 2X 0 X 0 2X X 2X 2X 0 generates a code of length 82 over Z3[X]/(X^2) who´s minimum homogenous weight is 144. Homogenous weight enumerator: w(x)=1x^0+50x^144+138x^147+78x^148+340x^150+468x^151+432x^153+840x^154+606x^156+1362x^157+764x^159+1812x^160+828x^162+2304x^163+938x^165+2064x^166+784x^168+1956x^169+714x^171+1440x^172+396x^174+600x^175+212x^177+192x^178+110x^180+6x^181+94x^183+52x^186+40x^189+38x^192+8x^195+12x^198+4x^201 The gray image is a linear code over GF(3) with n=246, k=9 and d=144. This code was found by Heurico 1.16 in 9.37 seconds.