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 X 1 1 1 1 1 X 1 X X 1 1 1 1 1 1 1 X X 1 1 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 2X^2 X^2 2X^2 X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 0 2X^2 0 X^2 2X^2 2X^2 X^2 0 0 0 X^2 X^2 2X^2 X^2 2X^2 0 X^2 X^2 X^2 X^2 X^2 2X^2 0 0 2X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 2X^2 2X^2 0 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 X^2 X^2 X^2 0 X^2 0 2X^2 2X^2 X^2 2X^2 0 X^2 X^2 0 X^2 2X^2 0 2X^2 X^2 X^2 2X^2 0 2X^2 X^2 X^2 0 2X^2 0 2X^2 X^2 X^2 0 2X^2 2X^2 X^2 2X^2 2X^2 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 0 X^2 2X^2 2X^2 2X^2 0 0 0 2X^2 2X^2 0 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 0 X^2 2X^2 2X^2 2X^2 0 0 X^2 X^2 X^2 0 X^2 2X^2 2X^2 X^2 0 2X^2 X^2 0 X^2 X^2 2X^2 X^2 2X^2 2X^2 0 X^2 X^2 2X^2 2X^2 0 0 X^2 2X^2 2X^2 0 0 0 0 0 0 X^2 0 0 X^2 2X^2 0 2X^2 0 0 2X^2 0 0 X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 0 X^2 0 X^2 0 2X^2 0 X^2 2X^2 0 2X^2 X^2 X^2 0 2X^2 0 2X^2 X^2 2X^2 2X^2 0 0 2X^2 2X^2 2X^2 X^2 X^2 2X^2 0 0 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 0 0 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 0 X^2 X^2 X^2 X^2 X^2 0 2X^2 0 X^2 0 0 0 2X^2 X^2 0 0 2X^2 2X^2 0 2X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 2X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 2X^2 0 2X^2 X^2 0 0 2X^2 0 0 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 X^2 X^2 0 2X^2 0 2X^2 2X^2 2X^2 X^2 X^2 X^2 0 X^2 2X^2 X^2 2X^2 2X^2 0 0 X^2 X^2 generates a code of length 65 over Z3[X]/(X^3) who´s minimum homogenous weight is 111. Homogenous weight enumerator: w(x)=1x^0+40x^111+110x^114+238x^117+6x^118+220x^120+72x^121+198x^123+360x^124+206x^126+960x^127+198x^129+14562x^130+178x^132+1152x^133+152x^135+384x^136+144x^138+142x^141+138x^144+90x^147+62x^150+44x^153+10x^156+6x^159+4x^162+4x^168+2x^177 The gray image is a linear code over GF(3) with n=585, k=9 and d=333. This code was found by Heurico 1.16 in 3.37 seconds.