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 X X 1 1 X X 1 1 1 1 1 1 1 1 X 1 X 1 X X 1 X X 1 1 1 1 1 1 X 1 1 1 1 1 0 X 0 0 0 0 0 0 0 0 0 0 0 0 2X X 2X X X 2X 0 X 0 0 X X 2X 2X 2X 2X X 2X 2X X X X 2X 0 X 2X X 0 X 0 X X X 2X X X 0 X 2X 0 2X X X 0 0 X X 0 X 2X X X 2X 2X X 0 X 0 0 0 X 0 0 0 0 0 0 0 0 X X X 2X 2X 0 2X X 0 2X 0 2X 0 X 0 X 2X 2X X 2X X 2X 2X 2X X 2X X X 0 0 X 2X X 0 2X 0 2X 0 X 0 2X 2X 0 2X 2X 0 0 2X 0 2X X 0 0 0 0 X X 2X X X 0 0 0 0 X 0 0 0 0 0 X X 2X 2X 2X 0 2X 0 0 X 2X 2X 2X X X 2X 0 2X X 2X 2X 0 2X 2X 2X X X 0 0 0 0 X X X X 2X 0 X 0 2X 2X 0 X X X 0 2X 2X 0 0 2X 0 2X 2X X X 0 X X 0 0 2X 0 0 0 0 0 X 0 0 0 X 2X 2X 2X X X 2X 2X X 0 X X 2X 2X X 2X 0 X 0 0 0 2X 0 X X 0 2X 0 X 0 0 X X X X 0 X 0 X 0 0 0 X 0 2X 0 X X 0 2X 2X 0 0 0 X X 2X 0 2X 0 X 2X 2X 0 0 0 0 0 0 X 0 0 2X 2X X X 0 2X 0 X X 2X X 0 0 2X X 2X X X 0 X 0 X X X 0 2X 2X X 0 0 2X 2X 2X X X 2X 0 2X X 2X X X X 2X X X X X X 0 X 2X X X 0 X 0 0 X 0 0 X X 0 0 0 0 0 0 0 X 0 2X X 2X X 2X 0 0 0 0 X 2X 2X 0 0 2X 0 X X 0 X 0 0 2X X X 2X 2X X 2X 2X X 0 2X 0 2X 0 X 2X 0 X X 2X X 0 X 0 X X 0 X 2X X X 2X 0 2X X X X X X 2X X 0 0 0 0 0 0 0 0 X X 0 X 0 X 0 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X X 0 0 X X 2X 2X X 0 2X X X X 0 0 0 2X 2X X 2X X X 0 2X 2X 0 X 0 X 0 0 X X 0 0 X X 2X 2X X 2X X X 0 X 2X 0 generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 120. Homogenous weight enumerator: w(x)=1x^0+58x^120+188x^123+352x^126+6x^128+448x^129+90x^131+452x^132+456x^134+464x^135+1110x^137+532x^138+2052x^140+492x^141+3210x^143+564x^144+3126x^146+586x^147+2070x^149+546x^150+870x^152+500x^153+132x^155+438x^156+328x^159+258x^162+176x^165+90x^168+42x^171+28x^174+10x^177+6x^180+2x^183 The gray image is a linear code over GF(3) with n=216, k=9 and d=120. This code was found by Heurico 1.16 in 13.3 seconds.