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 1 X X X X X X X X X X 1 1 X X X X X X X^2 X^2 X 0 X^2 0 0 0 0 X^2 2X^2 2X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 2X^2 0 2X^2 0 2X^2 0 X^2 2X^2 X^2 2X^2 2X^2 0 0 2X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 0 0 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 0 0 X^2 0 0 X^2 2X^2 0 2X^2 0 X^2 X^2 2X^2 2X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 2X^2 2X^2 X^2 X^2 2X^2 0 2X^2 0 X^2 X^2 0 2X^2 2X^2 0 X^2 0 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 0 2X^2 2X^2 X^2 X^2 0 X^2 2X^2 0 0 0 0 X^2 0 2X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 2X^2 2X^2 X^2 0 X^2 X^2 0 0 X^2 2X^2 X^2 X^2 2X^2 2X^2 0 0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 0 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 0 0 0 X^2 0 X^2 2X^2 0 0 2X^2 X^2 0 2X^2 2X^2 0 2X^2 X^2 0 0 X^2 0 0 2X^2 0 X^2 2X^2 0 2X^2 2X^2 0 0 0 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 0 2X^2 2X^2 0 X^2 0 0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 0 2X^2 0 0 2X^2 2X^2 X^2 0 0 0 2X^2 0 X^2 X^2 2X^2 2X^2 X^2 0 X^2 X^2 2X^2 X^2 X^2 2X^2 0 X^2 X^2 X^2 X^2 2X^2 X^2 0 0 2X^2 2X^2 2X^2 0 X^2 0 2X^2 generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 126. Homogenous weight enumerator: w(x)=1x^0+86x^126+174x^127+162x^128+36x^129+126x^130+648x^131+48x^132+648x^134+34x^135+120x^136+14x^138+36x^139+4x^141+30x^145+10x^153+4x^162+4x^165+2x^168 The gray image is a linear code over GF(3) with n=594, k=7 and d=378. This code was found by Heurico 1.16 in 0.495 seconds.