The generator matrix 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 X 1 1 0 X 0 1 1 0 1 1 0 X+1 1 1 0 1 X+1 X+1 X+1 1 0 X 1 1 0 X 1 1 0 0 X 0 0 0 0 0 0 X X X 0 0 X X 0 X 0 X X X X X 0 0 0 X 0 0 0 X 0 X X 0 0 X X 0 X 0 X X X 0 0 0 0 0 0 0 X 0 0 0 X X 0 X X X 0 0 X X 0 0 X X X X 0 0 0 0 0 X 0 X X X 0 0 0 X 0 X X X 0 X 0 0 0 X 0 0 0 0 0 0 X X 0 X 0 X X X X X 0 X X 0 0 0 0 0 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+144x^20+236x^24+120x^28+3x^32+8x^36 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 0.0198 seconds.