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 2X 1 1 1 1 0 1 X X 1 0 1 1 2X 2X 1 1 1 1 1 2X 1 0 1 1 1 1 1 X 1 1 0 2X 1 0 1 1 1 X 1 1 1 1 1 1 1 1 1 1 2X 1 X 2X 0 X 1 1 0 1 0 0 0 1 2 1 2X+1 2 2X+2 1 1 0 1 2X+2 1 X 2X+1 2X+1 2X 2X 1 2X+2 2 1 1 1 0 X 2 2X+2 1 X 2X+1 2X+1 X+1 0 X+2 1 1 2X+1 1 X X+2 1 2X 1 1 X+2 2X 2X+2 1 2X+2 1 X X+1 X 2X+1 2X+1 0 2X 2X+1 2X 1 2 X X+2 X X 1 1 2 X+1 2X 2X+2 2 0 0 X+1 2 1 2 X 1 1 1 1 0 0 0 1 1 2 2 2 1 2X 0 2X+1 2 2X+1 0 X+1 X+1 X+2 X+2 2X+2 2X 1 1 1 X X+2 2X X+2 X+1 2X 1 X+1 X X 2X 2X+1 0 2X+2 1 X+1 2 1 2X+1 X+1 2 2X 0 1 0 2X+2 1 X+1 2X+1 X 2X 1 1 X 1 X+2 X+1 1 2X 0 1 2X+1 X 1 X+2 0 0 2X+2 2X 2 0 0 1 2X+2 X+2 X+2 X+2 2X+1 1 X+2 1 2 X+1 2X+1 0 0 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 X 2X 0 2X X X 0 2X 0 0 2X 0 X 2X 0 X X X X 2X X 2X X 0 2X 2X 2X X 2X 0 0 0 2X 0 0 X X 2X 2X 2X X X X 2X 0 0 0 X 2X X 2X 2X X X X 0 0 0 0 0 X 0 X 2X 2X 2X 2X 0 X X 2X X 2X 2X 0 2X X 0 2X X 0 0 X 2X 0 X 0 0 0 2X X X X 0 2X X 0 0 X 2X X X 2X 2X X 0 0 X X 0 2X 0 0 0 0 2X X 2X X 0 2X X X 2X X X 0 2X 2X 0 2X 2X 2X X 2X X X 0 2X X 0 X X X 2X 0 0 0 0 0 2X X X 0 X 0 X X X 2X 2X 0 X 0 2X X 2X 0 X X X 2X 0 X 2X 2X 2X 0 0 X 0 0 0 X X 2X 2X X 2X 2X 0 0 2X X X 0 0 2X 2X X X 0 X 2X X 2X X 2X X X 2X 0 X X 0 X 2X X 0 2X 2X 2X X 2X 2X 2X X 0 2X 0 0 X 0 X generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 162. Homogenous weight enumerator: w(x)=1x^0+62x^162+48x^163+204x^164+332x^165+330x^166+672x^167+686x^168+372x^169+900x^170+794x^171+504x^172+1200x^173+862x^174+588x^175+1386x^176+840x^177+786x^178+1134x^179+826x^180+552x^181+1146x^182+714x^183+468x^184+972x^185+532x^186+360x^187+576x^188+454x^189+186x^190+402x^191+250x^192+126x^193+102x^194+130x^195+48x^196+36x^197+18x^198+6x^199+18x^200+28x^201+6x^204+10x^207+8x^210+2x^213+4x^216+2x^219 The gray image is a linear code over GF(3) with n=267, k=9 and d=162. This code was found by Heurico 1.16 in 9.06 seconds.