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 X 1 X 1 1 1 1 1 1 1 0 X 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X 2X 0 2X^2+X 2X 0 2X^2+X 2X X^2 2X^2+X 2X X^2+2X 0 2X^2+X X^2+X X^2+2X X^2 2X 0 2X^2+X X^2+X 0 2X X^2+2X X 0 X^2+2X 2X^2+X 2X^2 2X^2+2X X 2X 2X^2 X 2X^2+2X 0 2X^2 2X 2X^2+2X 2X^2 0 2X^2+X X^2+2X 2X 2X^2 X^2+2X X^2 2X X^2+2X 0 X X 2X^2+X 2X^2+2X X^2+X X^2+2X X^2 2X 2X^2+X 2X 2X^2 2X^2+X 2X^2 X^2+2X 0 0 0 0 X^2 0 0 0 0 2X^2 X^2 0 X^2 2X^2 2X^2 0 0 X^2 0 0 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 0 X^2 2X^2 X^2 0 X^2 2X^2 X^2 0 X^2 0 0 2X^2 2X^2 0 X^2 0 2X^2 X^2 0 X^2 0 0 X^2 X^2 2X^2 0 2X^2 X^2 0 X^2 0 0 0 0 X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 0 2X^2 2X^2 0 X^2 2X^2 X^2 X^2 0 2X^2 0 0 0 X^2 X^2 X^2 0 2X^2 X^2 2X^2 2X^2 X^2 0 2X^2 0 2X^2 X^2 0 2X^2 2X^2 X^2 0 2X^2 2X^2 0 0 X^2 0 X^2 2X^2 2X^2 2X^2 0 2X^2 0 0 0 0 0 2X^2 0 X^2 2X^2 X^2 X^2 0 X^2 2X^2 0 2X^2 0 2X^2 0 2X^2 2X^2 0 0 2X^2 X^2 0 0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 0 X^2 0 0 X^2 0 2X^2 X^2 2X^2 X^2 0 2X^2 X^2 2X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 2X^2 2X^2 2X^2 X^2 0 0 0 0 0 X^2 X^2 0 2X^2 X^2 0 0 X^2 X^2 2X^2 2X^2 X^2 X^2 0 2X^2 0 0 2X^2 X^2 2X^2 X^2 X^2 X^2 X^2 0 0 2X^2 0 X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 X^2 X^2 2X^2 2X^2 0 0 2X^2 0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 0 2X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 0 2X^2 generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 120. Homogenous weight enumerator: w(x)=1x^0+34x^120+54x^121+78x^122+142x^123+108x^124+162x^125+308x^126+174x^127+198x^128+442x^129+708x^130+210x^131+3646x^132+2160x^133+180x^134+6742x^135+2172x^136+222x^137+616x^138+186x^139+174x^140+242x^141+144x^142+144x^143+102x^144+84x^145+60x^146+44x^147+24x^148+24x^149+22x^150+18x^151+10x^153+6x^155+14x^156+16x^159+8x^162+2x^165+2x^189 The gray image is a linear code over GF(3) with n=603, k=9 and d=360. This code was found by Heurico 1.16 in 2.42 seconds.