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 2X 1 2X 0 X 1 1 2X 1 1 0 2X 1 0 2X 1 1 1 1 1 1 X 1 1 1 1 1 1 X 1 2X 1 1 1 0 1 1 1 1 2X 0 2X 1 1 2X 2X 1 X 1 1 1 1 1 X 2X 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 0 1 1 X 1 X X 0 1 2 2 X 1 X+1 2X 2X X+1 X+2 X 0 1 1 2 2X+2 1 X 2X+2 2 2 X+1 1 1 1 2 1 0 1 X+1 X 2 1 2X+2 2 0 1 2X X+1 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 2 X+1 2 1 1 2X+2 2X+2 1 2X+2 X+1 X+1 1 2X+2 2X+1 1 2 2X+2 2X+1 1 1 2X+1 X X+2 2X+1 2X+1 2X+1 X 2 1 X+1 2X+1 X+2 0 1 1 X 2X+2 X+1 X+2 2X X+2 2 X 0 1 1 2 1 X+2 2X X+2 0 X+2 2X 1 2X+1 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 2X X+1 2 2X 2X X 0 1 1 X X+2 2X+2 2 2X+1 2 0 1 1 X+2 X 2X+1 X X+1 X+1 2 2 1 1 2X+2 0 2X 0 0 2X X+2 2X+2 0 2X+1 X X+1 0 0 X+1 X+2 1 X+2 1 2X+1 2 X+1 X 2 0 2X+1 X 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 X+1 2X+2 2X+2 2X 2X+2 X 2X+2 2X+1 X+2 1 1 2X 2 0 X+1 0 X X+1 1 X+2 1 1 0 X 2 2X+1 2 2X+2 X+2 0 1 X 2 2 X 2X 2 2X+2 1 X 2X 2X+2 2X+1 X+2 X+1 X 2X X+2 X 1 0 1 2 X+1 2 X+2 generates a code of length 90 over Z3[X]/(X^2) who´s minimum homogenous weight is 163. Homogenous weight enumerator: w(x)=1x^0+258x^163+618x^164+156x^165+1206x^166+1332x^167+498x^168+1860x^169+2112x^170+556x^171+2616x^172+2598x^173+744x^174+2988x^175+3312x^176+870x^177+3396x^178+3552x^179+958x^180+3654x^181+3780x^182+810x^183+3420x^184+3282x^185+806x^186+2970x^187+2736x^188+570x^189+2166x^190+1698x^191+370x^192+1110x^193+756x^194+140x^195+456x^196+402x^197+48x^198+108x^199+54x^200+24x^201+24x^202+12x^203+8x^204+12x^205+2x^219 The gray image is a linear code over GF(3) with n=270, k=10 and d=163. This code was found by Heurico 1.16 in 84.2 seconds.