The generator matrix 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 0 1 1 1 X 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 2X 1 1 1 2X 1 2X 1 1 X 1 2X 1 1 1 0 0 1 1 2X 0 2X 0 1 X 1 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 2X+1 0 1 2 X 2X+1 1 2 2 X+1 2X 1 2X+2 2X+1 0 X+1 2X+2 1 2X+2 2X 2X+1 X 1 2X+1 0 2X 1 X+2 1 X X+2 1 1 1 X 2X 2 1 1 2X+1 2 1 1 1 1 X+1 1 X+2 X+1 0 2X 0 0 0 0 0 2X 0 0 0 0 0 0 0 0 0 0 X 0 X 2X X 2X X 2X 0 X 2X X X X 2X X 0 0 X 0 2X X X X X 2X X 0 X 0 X 2X 2X X 2X 0 0 2X 0 0 2X X X 2X 2X 2X 0 X 0 2X 0 0 0 X 2X 2X X X X 2X 0 0 0 0 X 0 0 0 0 0 0 0 2X 0 0 2X X 2X 0 X 2X 0 X X X 2X 2X 0 X X X X X 2X 0 X X 0 0 0 X X X 2X 2X 2X 2X 2X 0 2X 2X X 2X 0 2X 2X 2X 2X 0 X X 2X 2X 2X 0 2X X 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 X X 2X 0 X X 0 2X 0 X 0 X X 2X X 0 0 0 X X X X X 0 X 0 2X 2X X 2X X 0 0 0 2X 0 2X 2X X X 0 2X 0 0 X X X 2X 0 X 2X 2X X 2X X 0 0 0 0 0 0 2X 0 X 2X 2X 2X 2X 0 X 2X 2X 2X 0 2X 2X X 2X 0 0 X X 0 2X 0 0 X X 0 X X 0 0 0 X 2X 2X X X 0 X 0 X 2X 2X 2X 2X 0 2X 0 0 2X 2X X X X 2X X X 2X X 2X 0 X 2X 2X 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 0 2X 2X 2X X 2X 0 2X 0 2X 2X 2X 2X 0 2X 2X 2X 2X 0 X X X X 0 X 2X X 2X 0 0 2X 0 0 X 2X 2X 2X 2X 0 2X 2X 0 0 X 2X 2X X 0 2X 0 2X 2X X 2X 2X X X X 0 0 X 2X 0 X generates a code of length 74 over Z3[X]/(X^2) who´s minimum homogenous weight is 129. Homogenous weight enumerator: w(x)=1x^0+60x^129+12x^130+128x^132+150x^133+96x^134+216x^135+342x^136+402x^137+240x^138+726x^139+714x^140+196x^141+972x^142+1158x^143+156x^144+1266x^145+1578x^146+196x^147+1464x^148+1632x^149+200x^150+1602x^151+1680x^152+156x^153+1176x^154+1038x^155+152x^156+642x^157+354x^158+138x^159+300x^160+90x^161+100x^162+78x^163+6x^164+68x^165+18x^166+76x^168+38x^171+34x^174+18x^177+8x^180+6x^183 The gray image is a linear code over GF(3) with n=222, k=9 and d=129. This code was found by Heurico 1.16 in 8.19 seconds.