The generator matrix 1 0 0 0 1 1 1 1 1 2X 1 1 1 1 1 1 1 1 0 2X 1 0 X X 0 1 1 1 1 0 1 1 2X X 1 X X X 0 1 2X 1 1 1 1 0 2X 1 1 1 1 1 1 1 1 0 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 X 1 2X X 1 X 1 X 1 1 2X 2X X 1 1 0 1 0 0 0 0 2X+1 2X+1 X+1 1 2 X+2 2X 2X+2 1 X+2 X+2 X 1 1 2 1 1 0 1 2 X+1 2X+1 2X 1 2X+2 X+1 2X 1 2 1 1 1 1 2 1 2 0 2 X 1 1 2X+2 X+2 2X+1 X+2 X+1 X+1 2X+1 X+2 2X 1 2X 2X+1 1 2X 2X+1 2X+1 X+2 2 2X 2X X X 2X+1 1 X+1 2X 2 X X+1 1 1 X+1 2X X+2 1 2X 2X 1 0 1 0 1 0 0 1 0 0 X X 2X 0 0 2X 2X 2X+1 1 1 2X+2 2 X+1 1 X+1 1 X+2 X+1 1 2X+2 2X+1 X+2 X+2 2X+2 0 X+2 X+1 1 2X+1 0 2X+2 X+2 2 X 2X 2X 0 X+2 X+2 2X 1 1 2X+2 1 2X 2X+1 2X+2 2X+2 2X+1 2 0 X 1 2 X X+1 X+2 0 2X+2 X+1 X+1 2X 2X+1 X+2 2X+2 2X+2 X+2 2 0 1 X 1 2X+1 0 1 2X+2 2X+1 X+2 2 2X 0 2X X 2X+1 0 0 0 1 1 2X+2 2 1 0 X+2 0 2X+1 X 2X X X+1 0 1 2X X+1 2 2 X+2 1 1 X+1 1 X 2X+1 2X+1 2 2X+1 2 X+2 1 0 2 2X+1 2X+2 2X 1 X+2 2X 0 2 1 X+1 2X+2 X 2 2X+2 X+2 X 0 2X+1 1 X 2X+1 1 0 X+2 2X+2 2X+2 2 2X+2 X 1 X+2 2 2 2X X 1 2X 2X+1 2X+1 2X X+1 2 2X+2 0 2X+2 2 0 X 1 0 X X 0 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 2X 0 0 0 0 0 X 0 X X X X X 2X X X 2X X X X 2X 0 X 0 X X 2X 0 0 0 0 X 2X 0 X 2X X X 0 0 X 0 X X X 2X 0 2X X 2X 2X X 2X 0 X 0 2X 0 X 0 2X X 0 X X X 2X 2X 2X generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 164. Homogenous weight enumerator: w(x)=1x^0+252x^164+314x^165+336x^166+786x^167+656x^168+474x^169+900x^170+876x^171+582x^172+1068x^173+892x^174+552x^175+1314x^176+834x^177+648x^178+1206x^179+810x^180+498x^181+1008x^182+716x^183+516x^184+972x^185+624x^186+384x^187+654x^188+392x^189+186x^190+324x^191+294x^192+144x^193+180x^194+118x^195+42x^196+66x^197+18x^198+12x^199+12x^200+16x^201+6x^203 The gray image is a linear code over GF(3) with n=267, k=9 and d=164. This code was found by Heurico 1.16 in 8.94 seconds.