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 1 X 1 X 1 1 X 1 1 1 X 1 1 1 1 1 1 X 1 1 1 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 X^2 0 2X^2 0 2X^2 2X^2 X^2 2X^2 X^2 0 0 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 0 2X^2 0 X^2 X^2 0 X^2 0 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 0 0 X^2 2X^2 X^2 2X^2 X^2 0 2X^2 X^2 0 X^2 2X^2 X^2 2X^2 X^2 0 0 2X^2 0 0 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 0 X^2 0 X^2 2X^2 0 0 2X^2 2X^2 0 0 X^2 2X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 2X^2 X^2 0 0 0 X^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 X^2 0 0 2X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 2X^2 2X^2 2X^2 X^2 0 0 2X^2 2X^2 0 X^2 0 X^2 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 2X^2 X^2 2X^2 2X^2 X^2 0 2X^2 2X^2 2X^2 X^2 0 2X^2 0 2X^2 2X^2 0 X^2 2X^2 X^2 X^2 2X^2 X^2 0 X^2 X^2 0 generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 141. Homogenous weight enumerator: w(x)=1x^0+50x^141+126x^144+150x^147+354x^150+556x^153+4374x^154+546x^156+234x^159+34x^162+44x^165+12x^168+18x^171+24x^174+14x^177+8x^180+6x^183+2x^186+2x^189+4x^192+2x^216 The gray image is a linear code over GF(3) with n=693, k=8 and d=423. This code was found by Heurico 1.16 in 0.621 seconds.