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 1 X 0 X 0 1 1 1 0 X 1 1 1 1 0 X X X 0 1 1 1 1 1 1 1 1 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 0 0 X X X X+1 1 1 1 0 X X+1 1 1 1 0 X X 0 0 X X X+1 1 X+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 0 X X X X 0 0 0 X X X X X X 0 0 0 0 0 0 X X 0 0 0 X X generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+28x^52+2x^56+1x^64 The gray image is a linear code over GF(2) with n=102, k=5 and d=52. As d=52 is an upper bound for linear (102,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5. This code was found by Heurico 1.16 in 0.0244 seconds.