The generator matrix 1 0 1 1 1 1 2X^2+X 1 1 2X 1 1 1 0 1 1 1 1 1 2X^2 1 1 X 1 1 2X^2+2X 1 1 2X^2 1 1 1 1 1 0 1 1 1 1 1 1 2X 1 0 2X^2+X 1 1 1 2X^2+2X 1 1 0 1 1 2X^2+X 2X^2+2X 1 2X^2 2X^2+X X 0 1 1 1 X 1 1 1 1 1 0 1 1 2 2X^2+X 2X^2+X+2 1 2X^2+2X+1 2X 1 2X+2 X+1 0 1 2X^2+2 2X^2+2X+1 X+1 X+2 2X^2+X 1 2X 2X^2+X+1 1 2X^2+2X+2 2X^2 1 1 X 1 2X+1 2X^2+X+1 2 0 2X^2+2X+2 1 X+1 2X^2 2 2X^2+X+2 X^2+2X+1 2X^2+X 1 X+2 1 1 0 2X+2 2X^2+2X 1 X^2+2X 2X^2+X+2 1 2X+2 2X+2 1 1 2X+2 1 1 1 1 X^2+1 2X^2+2X+2 2X^2+2X 1 X^2+2 X^2+2 2X^2+2X X+1 X 0 0 2X 0 0 2X^2 2X^2 2X^2 X^2 0 0 2X^2 X^2+2X 2X^2+2X 2X^2+X X^2+2X 2X X 2X X^2+X X^2+2X 2X^2+X X 2X^2+X 2X^2+X X^2+X X^2+X 2X^2+X 2X^2+X X X^2+X 0 2X^2 2X^2+X 2X^2 2X^2 2X^2+X 2X^2+2X 0 X^2+2X 2X 2X 2X 2X X X^2 X^2 X 0 2X^2+2X X^2+2X 2X^2 X 2X^2 X^2+2X X^2+X 2X^2+2X 2X^2+2X 2X 2X^2+2X 2X^2+2X X^2+2X X^2+2X X 2X^2+X X X^2+X 2X X^2 X^2+X 0 0 0 X^2 0 0 0 2X^2 0 0 2X^2 X^2 0 0 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2 0 0 X^2 X^2 2X^2 0 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 0 0 X^2 X^2 2X^2 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 0 2X^2 0 X^2 X^2 2X^2 X^2 2X^2 0 2X^2 2X^2 2X^2 0 X^2 0 X^2 0 2X^2 0 0 0 2X^2 2X^2 2X^2 0 0 X^2 X^2 X^2 0 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 X^2 X^2 2X^2 0 2X^2 2X^2 X^2 X^2 0 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 0 0 X^2 X^2 X^2 2X^2 generates a code of length 70 over Z3[X]/(X^3) who´s minimum homogenous weight is 129. Homogenous weight enumerator: w(x)=1x^0+160x^129+186x^130+516x^131+1104x^132+1320x^133+1698x^134+2680x^135+2922x^136+3840x^137+5176x^138+5652x^139+6426x^140+6630x^141+5940x^142+4614x^143+4128x^144+2478x^145+1572x^146+852x^147+324x^148+168x^149+138x^150+102x^151+90x^152+172x^153+18x^154+24x^155+74x^156+12x^157+12x^159+6x^161+8x^162+2x^165+4x^171 The gray image is a linear code over GF(3) with n=630, k=10 and d=387. This code was found by Heurico 1.16 in 10.7 seconds.