The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 2X^2 1 1 1 1 1 2X^2 X 1 0 1 1 1 1 X 1 1 1 1 X 1 0 X 0 0 0 2X 2X^2+X 2X^2+2X X 2X^2+2X 2X^2 X 2X 2X^2+X 2X^2+2X 2X^2+X 0 X^2 X^2+X 2X^2+X 0 X 2X 2X 2X^2 X^2+2X 2X^2+2X 2X^2 2X^2 X 2X 2X^2+X 0 2X^2+X 2X^2+2X 2X X X 2X^2 2X^2 2X^2+X 2X^2+X 0 X^2+2X 2X 2X^2 2X^2 X^2+X X^2 2X X 2X^2 2X 2X^2+2X X^2+2X X X^2 2X^2+X 2X^2 X^2+2X X 2X^2+X X^2 2X^2+2X X X^2 0 0 X^2+2X X X^2+X 2X^2+X 2X^2 X 2X^2 X 2X 2X^2+X X 2X^2+X 0 0 X^2 2X^2+2X 2X 2X^2+2X 0 X 2X X^2+X 0 0 X 0 X^2 2X^2 X^2 2X^2 0 0 2X X X^2+2X X^2+2X 2X^2+X X^2+2X 2X^2+X 2X^2+X 2X X X^2+2X 2X^2+X 2X^2+X 2X^2+2X 2X^2+2X 2X^2+2X X 2X^2 2X^2+X X^2+X X^2+2X 2X^2+X 2X X^2 X^2 X X X^2 0 X^2+X 2X 2X^2+2X 2X^2+2X X^2 X^2+2X X^2 X^2+2X 0 X X^2+X 2X 2X X^2+X 2X^2+X 2X X^2 2X^2+X X^2+2X X^2 X^2 2X^2 2X^2 0 0 X^2+X X^2 X X 0 2X^2+2X 2X 2X^2+X 2X^2 2X^2+X 2X^2 X^2+X 2X^2 2X^2 2X^2+X X X^2+X X^2+2X 2X^2+2X 2X^2+2X 2X 2X^2+2X 2X 2X^2+X X X^2+2X 0 0 0 X 2X^2+2X 0 2X X^2+X X 2X X^2 2X^2 0 2X^2 X^2 X X^2+X 2X 2X^2+2X 2X^2+2X X^2+X X^2+X 2X X^2+2X 2X^2+2X X^2+X 2X^2+X X^2+2X 2X^2+X 0 2X X^2+2X X X 2X X^2+2X X^2+X X^2 X 2X^2 2X^2+X 0 2X^2 X^2 X 2X^2+2X X^2+2X 2X X^2+2X 2X^2+X X X 2X^2 2X X^2 2X^2 X^2+X 2X 2X^2 X X^2+X 2X X 2X^2+X X^2+2X 0 X^2 X^2+2X 2X^2+2X 2X^2+X 2X^2 2X^2+X X 2X^2 2X^2+2X X^2 0 X^2 2X^2+X X 2X 0 2X X 2X^2+2X 0 X^2+2X 2X^2+X 2X^2+X X^2 generates a code of length 90 over Z3[X]/(X^3) who´s minimum homogenous weight is 169. Homogenous weight enumerator: w(x)=1x^0+108x^169+240x^170+262x^171+462x^172+378x^173+440x^174+654x^175+768x^176+1008x^177+2328x^178+1680x^179+2784x^180+3324x^181+1584x^182+1156x^183+798x^184+192x^185+88x^186+222x^187+228x^188+140x^189+174x^190+132x^191+72x^192+90x^193+60x^194+84x^195+60x^196+48x^197+38x^198+18x^199+30x^200+24x^202+6x^203+2x^249 The gray image is a linear code over GF(3) with n=810, k=9 and d=507. This code was found by Heurico 1.16 in 3.1 seconds.