The generator matrix 1 0 0 0 0 1 1 1 X 1 1 0 1 X 0 1 1 1 X X 1 1 1 0 0 1 1 X 1 1 1 X 0 1 1 0 1 0 0 1 1 X 0 1 X 0 1 0 0 0 X X X 0 X+1 1 1 X+1 1 1 X+1 1 1 1 X X 0 0 1 1 1 0 X 0 X+1 0 1 X X X 1 0 0 1 X+1 0 0 1 X+1 1 0 0 1 0 0 0 0 0 0 0 0 X X X 0 X X+1 1 1 1 1 1 1 X+1 1 X+1 X+1 1 X X+1 X X+1 0 X 1 X+1 1 X X 0 X 1 1 X X 0 0 0 1 0 0 X+1 1 1 0 X 0 1 X+1 X+1 X+1 1 0 1 X+1 X X X+1 X+1 X X+1 X+1 X 1 1 X+1 1 1 X+1 1 1 X X X X X X 1 X+1 1 0 0 0 0 1 1 X+1 0 1 X X+1 X+1 X 1 X X+1 X X+1 0 1 X X+1 0 X+1 1 1 X+1 X+1 1 X+1 1 X+1 X+1 1 X+1 X+1 1 1 0 X+1 0 1 0 1 1 generates a code of length 45 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+315x^40+327x^44+219x^48+126x^52+33x^56+3x^60 The gray image is a linear code over GF(2) with n=90, k=10 and d=40. As d=40 is an upper bound for linear (90,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10. This code was found by Heurico 1.16 in 10.9 seconds.