The generator matrix 1 0 0 0 0 1 1 1 2X 1 1 1 1 1 0 1 0 1 1 X 1 1 0 1 1 X 1 1 1 1 1 1 1 X 1 2X 2X 0 X 1 1 2X 1 0 1 2X 1 2X 1 1 1 0 1 0 1 X 1 1 1 1 0 X 1 1 1 X 1 1 1 X 1 2X 1 2X 1 1 2X 1 1 1 1 2X X 0 1 1 X 1 1 0 1 0 0 0 2X 1 2X+1 1 0 X 2X+2 2 1 1 2X+2 1 2 1 1 2X+1 X+2 0 2X X 1 X+1 X+2 2X+1 0 2X X+2 X+1 1 1 1 1 1 0 2X+1 2X+1 1 2X+2 1 2 1 X X 0 X 2X 1 2X+2 2X X 1 2 X 2X+1 1 X 1 2 2X+2 X+1 1 2X+1 2X 2 1 2X 0 2X+1 1 X+1 X+2 1 2X+2 2X+2 X+2 X+2 1 1 1 1 2X 2X X+2 2X+2 0 0 1 0 0 0 0 0 0 X X X X 2X 2X 2X X 2X 2X X 2X 2X 2X 2X 2X 2 X+2 2X+1 X+2 X+2 1 1 1 2 X+1 2 2 1 1 2X+2 2X+2 1 2X+2 X+1 X+1 1 2 1 2X+2 X+1 2X+1 X+1 X+2 1 2X+2 2X+1 1 2X+1 X+1 X+1 1 2X+1 2X+2 X+2 2X X+1 2X 0 1 2 1 1 2X+2 2X 2X+2 X+2 2X+1 2X+2 1 X+2 0 2X+2 1 0 X X+1 1 X 2X 0 0 0 1 0 2X+1 1 2X+2 X+1 X+1 X+2 2X 2X+1 0 2 X+2 2 2X+2 2X 1 X+2 X 1 0 2 X+1 2 2X X+1 2X 2 2X+1 X+2 2X+2 X+1 2 2X 2X 2X X 0 1 1 X+2 2X+2 2X+2 0 2 1 2X+2 X+1 2X 2X X+2 2 X+1 2X+2 2X 2X 0 X+1 0 X+1 X X 2X+1 2 X+2 X 2X+1 2X 2 X+1 X X+2 X+1 0 2X+1 X+1 X X+2 X+1 2X+2 0 X 2X X+1 2X 1 0 0 0 0 1 2X+2 X X+2 X+2 2X+1 X X+1 2X X+1 2X+1 2X+2 0 2X 0 2X+1 2X+1 2 2X+1 2 2X+1 0 2X X X+1 1 2X+1 X+1 0 X+1 2X+2 2X+2 X+1 2X 2X+2 X 2X+2 2X+1 X+2 1 0 2X 0 X+1 X 2 X X+2 2X+1 X+2 2 2 1 1 2X+2 1 2X+1 1 2X+1 2X+2 X+2 0 X 1 2 1 0 2 0 X 2 X X+1 2X+1 2 0 2 1 1 1 X+1 2 2X 2X+1 0 generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 161. Homogenous weight enumerator: w(x)=1x^0+216x^161+316x^162+750x^163+858x^164+792x^165+1266x^166+1656x^167+1212x^168+1818x^169+2280x^170+1586x^171+2580x^172+2436x^173+1946x^174+2910x^175+3048x^176+2138x^177+3330x^178+2958x^179+2038x^180+2862x^181+2634x^182+2156x^183+2490x^184+2496x^185+1418x^186+1926x^187+1770x^188+864x^189+1188x^190+996x^191+542x^192+582x^193+378x^194+232x^195+126x^196+138x^197+60x^198+36x^199+6x^200+6x^202+2x^204+4x^207+2x^213 The gray image is a linear code over GF(3) with n=267, k=10 and d=161. This code was found by Heurico 1.16 in 85.5 seconds.