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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 X^2 2X 2X^2+X X 2X^2+2X 2X X^2 2X^2+X 2X^2+2X 0 2X^2+X 2X^2 2X^2 X 2X^2+2X 0 2X X 2X^2+X 2X^2 X^2 X^2+X X^2+2X X^2+X X^2+2X 2X^2+2X X^2+2X X^2 2X^2 X^2+X 2X X^2+X X^2+2X X^2+2X 2X 0 0 2X 2X^2+2X X^2 2X^2 2X^2 2X^2+X X^2+2X X^2+X 2X^2+X X^2+X X^2 2X^2+X X^2+X 2X^2+2X 2X^2 0 2X X X 2X^2+2X X^2+X X^2 2X^2+X 2X 0 X 2X^2+2X 2X 2X^2+X X^2+2X X^2+X 2X^2+2X X 0 0 X 2X^2+2X X^2 2X^2+2X X 2X^2+X X^2+2X X^2 2X^2+X 2X X^2 2X X^2+2X 0 2X^2 2X^2 X^2+X X^2+X X^2+X X^2+X 2X^2+X 2X^2+X X^2+2X 2X^2 2X^2 2X X^2+X 2X^2+X 2X 2X^2+2X 2X^2+2X 0 X^2 X^2+2X X X 2X X^2+2X 2X^2+2X 2X^2+2X 0 X^2 X^2+X X^2 0 2X^2+X X^2+2X 2X X 0 X X^2 X 2X^2+2X 2X 2X^2+X X^2 0 X^2+X X^2+X 2X^2 2X^2 2X^2 2X^2+2X X^2+2X 2X^2+X X X^2 0 X X^2+X generates a code of length 73 over Z3[X]/(X^3) who´s minimum homogenous weight is 144. Homogenous weight enumerator: w(x)=1x^0+558x^144+972x^146+504x^147+144x^150+6x^153+2x^216 The gray image is a linear code over GF(3) with n=657, k=7 and d=432. This code was found by Heurico 1.16 in 5.81 seconds.