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 1 1 1 1 1 1 X 1 1 X 1 1 1 1 1 1 1 X 1 X 1 X 1 1 1 1 1 0 X^2 0 0 0 0 0 0 0 0 X^2 2X^2 2X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 X^2 0 X^2 0 2X^2 X^2 0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 0 X^2 2X^2 2X^2 0 0 0 X^2 2X^2 X^2 X^2 X^2 0 2X^2 X^2 2X^2 X^2 0 X^2 2X^2 0 0 2X^2 2X^2 2X^2 0 X^2 2X^2 0 0 0 2X^2 0 2X^2 0 2X^2 2X^2 0 0 0 X^2 0 0 0 0 X^2 2X^2 2X^2 2X^2 0 0 2X^2 X^2 2X^2 X^2 0 X^2 X^2 0 2X^2 2X^2 0 X^2 X^2 2X^2 0 X^2 0 2X^2 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 2X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 2X^2 X^2 X^2 0 2X^2 0 X^2 X^2 X^2 0 0 0 0 2X^2 0 0 0 0 X^2 0 0 X^2 2X^2 0 2X^2 0 0 2X^2 X^2 X^2 2X^2 0 X^2 0 2X^2 0 2X^2 2X^2 0 2X^2 0 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 0 2X^2 0 2X^2 X^2 0 2X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 0 0 0 X^2 0 0 X^2 2X^2 X^2 2X^2 0 X^2 2X^2 X^2 X^2 0 0 X^2 0 0 2X^2 2X^2 0 2X^2 0 0 0 0 X^2 0 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 0 2X^2 2X^2 0 2X^2 X^2 0 2X^2 2X^2 0 X^2 2X^2 0 2X^2 X^2 0 X^2 0 X^2 0 2X^2 2X^2 0 0 2X^2 2X^2 X^2 0 X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 X^2 X^2 X^2 0 X^2 0 2X^2 2X^2 X^2 X^2 2X^2 0 0 X^2 0 X^2 2X^2 2X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 0 2X^2 0 X^2 0 0 2X^2 X^2 2X^2 0 2X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 2X^2 X^2 2X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 0 2X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 2X^2 2X^2 X^2 0 2X^2 generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 132. Homogenous weight enumerator: w(x)=1x^0+90x^132+114x^135+104x^138+432x^140+86x^141+324x^143+4442x^144+486x^146+68x^147+216x^149+40x^150+34x^153+22x^156+34x^159+24x^162+14x^165+14x^168+2x^171+6x^174+6x^177+2x^201 The gray image is a linear code over GF(3) with n=648, k=8 and d=396. This code was found by Heurico 1.16 in 0.552 seconds.