problem with newey west algorithm in matlab

Hey, i have a question about a function file from this forum that calculates the newey west standard error of a regression. This is the file:

    *_function se = NeweyWest(e,X,L)
    % PURPOSE: computes Newey-West adjusted heteroscedastic-serial
    %          consistent standard errors
    %---------------------------------------------------
    % where: e = T x n vector of model residuals
    %        X = T x k matrix of independant variables
    %        L = lag length to use
    %
    %        se = Newey-West standard errors
    %---------------------------------------------------

    indexxx = sum(isnan(X),2)==0;
    X = X(indexxx,:);
    e = e(indexxx,:);

    [N,k] = size(X);
    k = k+1;
    X = [ones(N,1),X];

    if nargin < 3
    % Newey-West (1994) plug-in procedure
    L = floor(4*((N/100)^(2/9)));
    end

    Q = 0;
    for l = 0:L
        w_l = 1-l/(L+1);
        for t = l+1:N
            if (l==0)   % This calculates the S_0 portion
                Q = Q  + e(t) ^2 * X(t, :)' * X(t,:);
            else        % This calculates the off-diagonal terms
                Q = Q + w_l * e(t) * e(t-l)* ...
                    (X(t, :)' * X(t-l,:) + X(t-l, :)' * X(t,:));
            end
        end
    end
    Q = (1/(N-k)) .*Q;

    se = sqrt(diag(N.*((X'*X)\Q/(X'*X))));

    end_*

I want to know the newey west standard error of a regression where i regress the equity premium on a constant only. This means my vector X is a 778x1 vector containing ones. However, this results in a standard error of NAN, because (X'*X)\Q/(X'*X) produces a NAN. At this point, X is a 2x2 vector with value 778 and Q is a 2x2 vector containing 4.9*10^-8. Matlab says: "Warning: Matrix is singular to working precision. > In NeweyWest at 43". Does anyone know how i can get newey west standard errors out of this regression?

Donald