Help in finding the inverse of a particular matrix

I need help in finding the inverse of this matrix:
[,1] [,2] [,3] [,4]
[1,] 161 349 662 879
[2,] 349 1147 1790 1851
[3,] 662 1790 3062 3464
[4,] 879 1851 3464 5395

If i use the "inv()" function (matlib package) the following message appears: "Error in Inverse(X, tol = sqrt(.Machine$double.eps), ...) :
X is numerically singular"
However, the determinant is not 0.
'> det(X)
[1] -3.66251e-06'
I guess R approximates det to 0 since its a very small value. how can i solve this problem?

I think its the opposite, the determinant is zero and not a small number, and so the matrix is singular. (I typed your matrix into wolfram alpha)