The generator matrix 1 0 0 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 0 X 0 1 0 X 1 X+1 1 X 0 0 1 X+1 X+1 X 1 0 X X+1 1 1 1 0 0 1 1 X+1 X 1 X+1 1 X 1 0 X+1 0 X X+1 X 1 0 X X 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+32x^20+24x^22+6x^24+1x^32 The gray image is a linear code over GF(2) with n=42, k=6 and d=20. As d=20 is an upper bound for linear (42,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6. This code was found by Heurico 1.16 in 0.00142 seconds.