The generator matrix 1 0 0 0 1 1 1 2X^2 1 1 1 1 1 1 X^2+2X 1 1 1 1 1 1 1 1 1 2X 1 1 1 1 1 X^2+X 1 1 1 2X^2+2X 1 2X^2 1 1 X^2 1 0 2X^2+2X 0 0 X 1 1 1 X^2+X 2X^2+X X 1 X^2+2X 0 1 1 1 1 2X X^2+X 2X^2+X 1 1 1 1 1 1 1 0 1 0 0 2X^2 1 X^2+1 1 X X^2+X 2X^2+2X+2 X^2+2 2X^2+X+1 X^2+X+1 1 2X+1 2X^2+2X 2X X+2 2X^2+2X+1 2X^2+X+2 X^2+2X+1 2X^2+2X X 1 X+2 X+1 2X^2+X+2 2 X^2+2X+2 0 2X^2+2X+2 2X 1 1 2X^2 1 X^2+X 2X^2+X+2 1 2X+2 1 X^2+2X 1 1 1 X 0 1 2X^2+2X 1 X^2+2X 2 X^2 1 X^2+2 0 2X^2 2X+1 2X^2+2X 1 1 X^2+2X X+2 2X^2+X 2X^2+2 0 X^2+X+1 2X^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 X^2+2X+2 X^2+2 2X+1 X X^2+X+2 2X^2+X+1 2X^2+X 2 X^2+2X X^2 2X+1 0 X^2+2X+1 2X^2+2 2X^2 2 2X^2+2X+2 1 X^2+2X 2X^2+2 X+1 2X^2+X+1 X^2+1 X^2+1 2X+2 1 X^2+2X 2 2X^2+X+2 1 2X^2+2X+2 X^2+2X+1 2X^2+2 X+2 2X^2+2X+1 X 1 2X^2+2X 1 2X X^2 X^2+2X+2 X^2+2X 2X 2X^2+X X^2+X+1 2X^2+2X X+2 2X^2+1 2X^2+2X X^2+2 2X^2+1 2X^2+X X^2+2X+1 X^2 2X^2+2X 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^2+2X+1 X^2+2X X^2+2 2 X^2+X+2 X^2+2X+2 2X^2+2X+1 X^2 2X^2+2X+2 2X^2+X+1 2X 2X^2+2X+2 X^2+X+1 X 2X^2+X X^2+2X+1 X^2+2X+2 1 X+2 1 X^2+2X+1 2X^2+1 2X^2+2X X^2+X X^2+2X+2 2X^2+2X+1 2X^2+1 2X^2+2X 2X^2+2X+1 2X^2+X+2 2X^2+2X+2 X+2 X^2 X^2 2X^2+1 X+2 X^2+X+2 2X+1 X^2+2X 2X^2+2X 1 2X^2+2X+1 2X^2+1 2X^2+X 2X^2+X+1 2X+1 1 2X^2+X+2 X+1 2X X^2+2X+1 X^2+X+1 X^2+X+1 X X^2 2X generates a code of length 69 over Z3[X]/(X^3) who�s minimum homogenous weight is 126. Homogenous weight enumerator: w(x)=1x^0+364x^126+900x^127+3330x^128+5942x^129+8484x^130+11826x^131+18046x^132+21534x^133+29454x^134+38288x^135+41364x^136+46620x^137+56230x^138+51780x^139+50856x^140+48976x^141+34470x^142+24870x^143+18468x^144+9252x^145+6000x^146+2290x^147+1272x^148+438x^149+136x^150+48x^151+72x^152+38x^153+18x^154+30x^155+32x^156+6x^157+6x^158 The gray image is a linear code over GF(3) with n=621, k=12 and d=378. This code was found by Heurico 1.16 in 558 seconds.