The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 1 X 1 1 X X 1 1 X 1 X 1 1 X 1 1 1 1 1 1 1 1 0 1 1 1 X X 1 X 1 X 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X 2X 2X 2X 2X 2X 2X X X X 2X 0 0 X 2X X 0 X X 2X X 2X 2X X 0 2X 0 X 2X X X 0 2X 0 X X 2X X X 2X 2X X 2X 2X 0 0 0 X X 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 0 0 2X 2X 2X X X 2X 0 X 0 X 2X X X 2X 0 X X 0 2X 0 2X 2X 0 2X X 2X 0 2X X 2X 2X 0 2X 2X 0 2X 0 X X X X 0 2X 0 X 2X X 0 X X X X 2X 0 2X 2X 0 0 0 X 0 0 0 0 0 0 0 0 X X 0 0 X X 2X 0 2X 2X 2X 2X X 0 2X 0 2X X 0 2X X 0 X 2X X 2X 2X 0 2X X X 2X X 2X X X 0 0 2X 2X 2X 2X X 0 0 X X 0 0 0 0 2X 2X 0 0 2X X 0 X 0 2X 2X X 0 2X X 0 0 0 0 0 X 0 0 0 0 X 2X 2X 2X 2X 0 X X 0 2X X 0 0 X 0 2X X 2X 0 X X 2X 0 2X 2X 2X 2X X 0 2X 0 2X 0 2X X 0 X 0 X 0 2X 0 X 2X 2X 2X 0 0 X 2X X 0 0 X 0 2X 2X X 0 2X 0 X 2X 0 X X 0 X 0 2X 0 0 0 0 0 X 0 0 X 2X 0 2X 2X X 0 0 X 0 X X 2X 0 2X 0 0 0 2X 2X X 0 0 2X 2X 2X X X 2X 0 X 2X 2X 2X 0 X X 2X X 0 X 0 X 0 2X 0 X 2X 0 2X 2X 2X 0 2X 2X 0 2X 2X 0 X 0 2X 0 0 X 0 X X 0 0 2X 0 0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X X X 0 X 0 0 X 0 X 0 2X 0 0 2X X 2X X 0 2X X X X 0 0 2X 0 0 0 X X X 2X 0 0 X X 2X 2X X 2X X X 0 X 0 2X X 0 2X 2X X 2X 2X 2X X 0 X X X 2X 0 X 0 X 0 0 0 0 0 0 0 X 2X 2X 2X 2X X 0 X X 2X 2X X 2X 0 0 2X X 0 X X 2X X X 0 0 0 X X 2X X X 0 X 0 2X X 0 2X X 0 2X 2X X X X 0 0 0 2X 0 0 2X 2X 2X 2X 0 2X X X 0 0 2X X 0 0 X 0 2X 0 0 X X generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 135. Homogenous weight enumerator: w(x)=1x^0+110x^135+296x^138+406x^141+492x^144+892x^147+1430x^150+2226x^153+3192x^156+3678x^159+2894x^162+1784x^165+912x^168+456x^171+340x^174+246x^177+152x^180+74x^183+68x^186+12x^189+10x^192+10x^195+2x^198 The gray image is a linear code over GF(3) with n=237, k=9 and d=135. This code was found by Heurico 1.16 in 15.4 seconds.