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 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 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X 0 0 0 0 0 0 0 0 0 0 X X 0 X 0 X 0 X X X 0 X X X 0 X 0 X X X X X 0 0 0 0 X 0 0 0 0 0 0 0 X X X X X X X X X 0 X X 0 0 X X X X 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X 0 0 X X 0 0 X X X X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X 0 X X 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 0 0 X X X X X X X X 0 0 0 0 0 0 0 0 X X X X X X X X 0 0 0 0 0 0 0 0 X X X X X X 0 0 X 0 X 0 0 X X 0 0 X X 0 0 X 0 X X X 0 0 0 0 0 0 0 0 X 0 X X X 0 0 0 0 X X X X 0 0 0 X X X X X X 0 0 0 0 X X 0 0 X X X X 0 0 0 0 X X X X 0 0 0 0 X X X X 0 0 0 0 X X X X 0 0 0 0 X X X X 0 0 0 0 0 0 X X X X X X 0 X X 0 X X 0 X 0 0 0 X 0 0 0 0 0 0 0 0 0 X X 0 X X 0 X X X 0 0 X 0 X X X 0 0 X 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X 0 X X X 0 0 0 0 0 0 X X 0 X X X 0 0 X X X 0 0 0 generates a code of length 98 over Z2[X]/(X^2) who´s minimum homogenous weight is 96. Homogenous weight enumerator: w(x)=1x^0+31x^96+64x^98+31x^100+1x^196 The gray image is a linear code over GF(2) with n=196, k=7 and d=96. As d=96 is an upper bound for linear (196,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7. This code was found by Heurico 1.16 in 0.2 seconds.