The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X 0 0 0 X X X 0 0 0 X 0 X X X 0 0 0 X X 0 0 X 0 X X X 0 0 0 X X X X 0 0 0 0 X X 0 0 0 0 X X 0 X X 0 X X 0 0 X X 0 0 X X 0 0 generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 20. Homogenous weight enumerator: w(x)=1x^0+18x^20+8x^22+4x^24+1x^40 The gray image is a linear code over GF(2) with n=42, k=5 and d=20. As d=20 is an upper bound for linear (42,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5. This code was found by Heurico 1.16 in 0.00127 seconds.