The generator matrix 1 0 0 0 1 1 1 2X^2 1 1 1 1 1 2X 1 1 1 1 2X^2+2X 2X^2+X 0 1 1 X^2+X 1 1 X X 2X 1 1 1 1 1 1 1 1 2X^2 1 X 1 1 1 1 1 X^2+2X 1 X^2 1 2X^2 1 1 1 1 1 1 2X^2+X 1 1 2X^2+X 2X^2+X 1 1 1 X^2+2X 1 2X^2 2X^2+2X 1 2X 1 0 1 0 0 2X^2 1 X^2+1 1 X X^2+X 2X^2+2X+2 X^2+2 X^2+X+1 1 X^2+2 2X^2+2 2X^2+2X+1 2X^2+2X+2 1 1 2X^2+X X 2X^2 1 X^2+2X+2 2X 1 2X^2 1 X^2+X+1 X^2+X+1 2X^2+1 2X+2 X^2+1 X^2+X+2 X^2+1 2X^2+2X+2 1 2X^2+X 1 2X^2 2X+1 2X^2+X+1 X^2+X+1 2X^2+X+1 1 2X^2+X+2 1 2X^2+X 1 2X+2 X^2+2X X^2+2X 2X 2X^2+2X+1 X^2+X 1 X^2+X+2 2X^2+2 1 X^2+X X+1 2X^2+2 2X^2+2 1 2X^2+X 1 1 2X^2+2X X^2+X X^2+X 0 0 1 0 2X^2+2X+1 2X+1 2X^2+X+2 2X^2+2X+1 X+1 X+2 2X^2 2X^2+X+1 2X^2+X+2 2X+2 X^2+2 X^2+2X 2X+1 X+1 2X^2 2X^2+X+1 1 2X^2+2 X^2+1 X^2+X+2 X^2+2X+2 2 2 1 2X+1 X^2+2X+2 X^2+X 2X^2+1 X^2+2X 2X^2+2X 2X^2+2X+2 X^2 2X^2+2X+1 2X X^2+2X 2X X^2 X^2+X+2 X+1 2X^2+2 0 2 X^2+1 X^2+1 X^2+2X+1 X+1 X^2+2 2X^2 2X^2+X+2 X^2+X+1 2X+2 X^2+X+2 0 X^2+X 2X^2+2X+1 2X^2+2X X^2+2X X^2+1 2X X^2+X X+2 2 X^2+2X 2X^2+2 0 1 2X^2+X 0 0 0 1 2X^2+2X+2 X^2 X^2+2X+2 X^2+2X+2 1 X^2+X 2X^2+1 2X^2+2X 2X^2+2X+1 0 2X^2 X+2 2X^2+2 2X^2+X+1 X^2+2X+2 2X^2+X+1 2X^2+X+1 X^2+2X+2 2X 2X^2+X+2 2 X+1 X^2+2X+1 2X+2 2X^2+X 2X^2+X X^2+2X 2X^2+X+1 2X 2X^2+2 X^2+2X+1 2X+1 X^2+2X+2 1 2X+1 X 2X^2+2 2X^2+2X+1 2X^2+2X+2 X^2 X+1 2X^2 2 X 2X^2+2X+1 2X+1 2X^2+X+2 X^2+X X^2+1 2X^2 X^2+2X+2 2X^2+2X+2 2X^2+2X+2 2 2X^2+X+1 X^2+1 1 X^2+2X+2 X+1 2X+1 2X X^2+2X X 2X X^2+2X X^2+2 X^2+X generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 130. Homogenous weight enumerator: w(x)=1x^0+438x^130+1110x^131+3502x^132+6024x^133+8766x^134+12684x^135+17784x^136+22632x^137+27554x^138+38430x^139+42174x^140+46766x^141+53604x^142+53394x^143+48710x^144+47310x^145+35256x^146+25288x^147+18576x^148+10416x^149+6082x^150+2784x^151+1104x^152+634x^153+126x^154+90x^155+60x^156+60x^157+12x^158+26x^159+12x^160+6x^161+8x^162+12x^163+6x^166 The gray image is a linear code over GF(3) with n=639, k=12 and d=390. This code was found by Heurico 1.16 in 577 seconds.