The generator matrix 1 0 0 1 1 1 X 1 1 1 0 1 X 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 1 0 X X+1 X 1 1 1 X+1 X+1 X 1 1 1 0 1 1 1 0 0 1 1 1 0 1 X X+1 0 1 1 X+1 X 0 0 1 X 1 1 1 0 1 X+1 0 0 0 X 0 0 0 0 0 0 X X X 0 X X X 0 X 0 0 X X 0 0 0 0 0 X 0 0 X X X 0 X X X X 0 X 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X X 0 X X X 0 X X generates a code of length 24 over Z2[X]/(X^2) who´s minimum homogenous weight is 20. Homogenous weight enumerator: w(x)=1x^0+106x^20+124x^22+114x^24+40x^26+86x^28+28x^30+13x^32 The gray image is a linear code over GF(2) with n=48, k=9 and d=20. As d=20 is an upper bound for linear (48,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9. This code was found by Heurico 1.16 in 6.87e-008 seconds.