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 X 1 1 X 1 1 X 1 X 1 1 1 1 1 X 1 1 1 1 1 1 1 X 1 X 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 X^2 0 2X^2 2X^2 0 0 0 X^2 2X^2 X^2 0 2X^2 X^2 2X^2 X^2 2X^2 0 2X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 0 0 0 2X^2 2X^2 2X^2 0 X^2 0 0 0 2X^2 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 2X^2 0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 0 0 2X^2 2X^2 0 X^2 X^2 0 X^2 X^2 X^2 2X^2 X^2 X^2 0 2X^2 2X^2 X^2 0 X^2 X^2 2X^2 0 X^2 X^2 X^2 0 0 X^2 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 0 2X^2 2X^2 X^2 2X^2 X^2 0 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 0 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2 0 2X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2 0 2X^2 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 0 2X^2 0 2X^2 X^2 0 2X^2 X^2 2X^2 X^2 2X^2 0 2X^2 2X^2 0 X^2 2X^2 X^2 0 2X^2 2X^2 0 2X^2 2X^2 2X^2 0 0 2X^2 0 0 2X^2 0 2X^2 2X^2 0 2X^2 0 X^2 X^2 2X^2 0 2X^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 0 X^2 X^2 0 X^2 0 0 X^2 2X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 0 2X^2 2X^2 2X^2 2X^2 0 2X^2 X^2 0 0 0 2X^2 X^2 2X^2 2X^2 0 2X^2 X^2 0 generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 141. Homogenous weight enumerator: w(x)=1x^0+166x^141+176x^144+204x^147+522x^150+4374x^152+492x^153+336x^156+156x^159+32x^162+44x^168+16x^171+24x^177+10x^180+6x^186+2x^207 The gray image is a linear code over GF(3) with n=684, k=8 and d=423. This code was found by Heurico 1.16 in 56.6 seconds.