The generator matrix 1 0 0 0 1 1 1 1 1 0 1 X 1 1 1 1 X 1 0 2X 1 1 1 0 2X 1 1 1 1 X X X 1 1 1 1 2X 1 1 X 0 0 1 1 1 1 1 1 1 1 2X 1 1 1 X 1 1 1 X X 1 1 1 2X 2X 1 2X 0 1 1 1 1 1 0 X 1 1 1 1 1 1 1 1 1 2X 2X X 2X 1 1 0 1 0 0 0 0 2X 2X 0 2X 2X 2X 2X 1 X+1 2 1 X+2 1 1 X+2 2 1 1 1 2X+2 2X 2X+2 2X+2 1 1 1 X+2 2X X+1 2X+1 1 2X+1 0 2X X 1 1 0 X+2 2X+1 1 X+1 2 2X X X+2 2X+2 0 1 2X 2X 2X+1 1 2X X+1 1 2 1 1 1 1 1 2X+1 2X 1 0 0 0 0 2 X+1 2X 2X+1 0 2X+1 2 0 1 1 1 1 2X 2X+2 X+2 0 0 1 0 0 X 2X+1 2 2X+1 1 X+2 1 X+1 1 1 2X+1 2 X+1 2 2X 2X X+2 2 0 2 2 X+2 2X+2 0 2X X+1 X+1 2X+1 2X 0 X X+1 2X+1 X 0 1 X+1 2X+2 X+1 X+1 0 2X+2 2 X+1 X+1 1 X+2 2 X+2 X+1 2X+1 2X X 0 1 0 2X+1 X+2 X X+2 X+1 1 X+2 2X+1 1 2X 2X+2 1 1 X 1 1 2X 2X+2 X+2 1 X+2 2X+2 0 X 0 1 1 X+1 0 0 0 0 1 1 2X+2 2X 0 X+1 1 2X+2 X+2 2 X+2 2X 2X+1 X+1 X X 2 2X+1 1 X+1 2X+1 X+2 2X+2 2X+1 0 2X+2 X 2 X+1 X+2 2X+2 1 2X 2X+2 1 0 1 2X+2 X+1 2X+2 X+2 X+1 2 X 2X 0 X X 2X+2 2X X+1 0 0 X+1 X 2X+2 1 X+1 2X 1 1 X+1 1 X+2 2 2 X X 2 1 2X+1 1 X+1 2X 2X+2 X+1 X+2 X+1 2X 0 X+1 0 0 0 1 2 2X 0 0 0 0 2X 2X 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 2X 0 0 2X 2X X X X 0 X 0 X X 2X X 0 X 0 X X X X X 2X 2X 0 0 0 2X X 0 X 0 2X X 2X 0 2X X 0 2X X 2X X 0 X 2X 2X 0 0 0 0 0 0 0 0 2X 2X X X 2X 2X X 0 0 0 2X 2X X 0 X 0 2X generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 166. Homogenous weight enumerator: w(x)=1x^0+276x^166+312x^167+352x^168+576x^169+684x^170+640x^171+846x^172+972x^173+620x^174+900x^175+1104x^176+682x^177+972x^178+912x^179+682x^180+984x^181+972x^182+656x^183+930x^184+780x^185+586x^186+720x^187+702x^188+358x^189+504x^190+378x^191+336x^192+342x^193+282x^194+136x^195+144x^196+150x^197+18x^198+78x^199+18x^200+24x^201+18x^202+24x^203+6x^204+2x^207+2x^210+2x^213 The gray image is a linear code over GF(3) with n=270, k=9 and d=166. This code was found by Heurico 1.16 in 11.4 seconds.