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 X X X 0 0 0 1 1 1 1 X X X 0 0 0 1 1 1 1 X X 0 X 0 X 0 X 1 1 1 1 X X X X 0 0 0 X 1 1 X X 0 0 0 X 0 X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 X X X X 0 0 0 X X 0 X X X X 0 0 0 X X 0 0 0 X X X X 0 0 0 X X 0 0 X X X X 0 0 0 0 X X X X 0 0 X X 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 X X 0 0 X X 0 X X 0 X X 0 0 X X 0 X X 0 0 X X X X 0 0 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X generates a code of length 70 over Z2[X]/(X^2) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+12x^74+2x^76+1x^80 The gray image is a linear code over GF(2) with n=140, k=4 and d=74. As d=74 is an upper bound for linear (140,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4. This code was found by Heurico 1.16 in 0.0782 seconds.