The generator matrix 1 0 1 1 1 0 1 1 X 1 1 X 1 1 0 1 1 0 1 1 1 1 X X X X 0 0 1 1 1 1 0 X X X 0 1 1 1 1 0 X 0 1 1 0 X+1 1 X X+1 1 X 1 1 0 X+1 1 0 X+1 1 X X 1 1 1 1 0 X X 0 0 X X+1 1 1 1 0 X X 0 X+1 X 1 1 1 0 0 X X 0 X X X X 0 0 0 0 0 X X X 0 X 0 X 0 X 0 X X X X 0 0 0 0 X X 0 0 0 X X X X 0 0 generates a code of length 43 over Z2[X]/(X^2) who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+28x^44+3x^48 The gray image is a linear code over GF(2) with n=86, k=5 and d=44. As d=44 is an upper bound for linear (86,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5. This code was found by Heurico 1.16 in 0.0132 seconds.