The generator matrix 1 0 0 1 1 1 1 1 1 1 1 0 2X 1 2X 1 X 1 1 1 1 0 1 1 1 2X X 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 2X 1 X 2X 0 1 1 1 1 1 X X 1 1 X 1 1 X 1 1 0 1 0 1 0 1 2X X 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 2X+1 2X 2X 1 2X+2 2 1 1 1 0 X 2 X+2 2X 2X 2X 2X+2 1 0 2X+1 1 1 X+2 0 2X+1 2X+1 0 X+2 1 X 1 X+1 2X+2 2X 2X+2 X+2 X 1 X 2 1 2X+2 0 2X 2 2X+1 0 1 1 2X+1 1 X+2 0 1 X X 1 2X+2 X+1 X+1 0 2X 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 1 1 X X+2 2X X+2 X+1 2X 1 X+1 0 2X 1 X+2 2 0 X+2 0 X+1 2X+1 X+1 2X+1 2 2 1 2X+1 X+2 1 2X+2 2X X+2 0 X+2 X+2 1 X+2 2 X+2 2X+2 X+2 2 1 2X+1 0 1 1 2X+2 2 1 X+2 1 X X+2 X 2 2X X+1 X 0 2X+1 0 0 0 2X 0 0 0 0 0 2X 2X X 2X 2X X 0 2X 2X 2X X 0 X 2X 0 0 0 X 0 2X 2X 0 2X X 0 X 0 X X 0 2X 2X X X X X X X X X 0 X 2X X 0 X 2X X 0 2X 0 2X 2X 2X X X X X 2X 2X 0 2X 2X X 0 2X X 0 X 0 X 2X 0 0 0 0 X 0 X 2X 2X 2X 2X 0 X X 2X X 2X 0 2X 2X X 0 2X X 0 0 X 2X 0 X 2X 2X 0 X 2X 2X 0 X 0 X X 2X 0 X 2X 2X X 0 X 2X X 0 0 2X X 2X 0 0 0 0 0 X X 2X 2X 0 X X X X X X 2X X 2X X X 2X X X 0 0 0 0 0 0 2X X X 0 X 0 X X X 2X 2X 0 0 X 2X X 2X 0 X X X 2X 0 X 2X 0 0 0 2X 0 2X 0 0 X 0 0 X 2X 2X X 0 X 2X 2X 2X 0 X X X 2X X 0 X 2X 0 0 X X 2X 0 0 2X 2X 0 X 0 2X 2X X 2X 0 0 X 0 2X 2X generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 147. Homogenous weight enumerator: w(x)=1x^0+108x^147+90x^148+300x^149+382x^150+354x^151+792x^152+672x^153+594x^154+1110x^155+788x^156+570x^157+1104x^158+922x^159+558x^160+1284x^161+926x^162+486x^163+1230x^164+920x^165+588x^166+1356x^167+808x^168+534x^169+858x^170+524x^171+336x^172+408x^173+278x^174+150x^175+198x^176+102x^177+66x^178+90x^179+68x^180+42x^181+6x^182+24x^183+6x^184+12x^185+18x^186+14x^189+6x^192 The gray image is a linear code over GF(3) with n=243, k=9 and d=147. This code was found by Heurico 1.16 in 8.06 seconds.