I think you cannot integrate stochastic delay differential equations easily with Matlab. Using dde23 with an additional gaussian term in the function is wrong in general, since there is no warranty of convergence.
Unfortunately you will probably have to develop your own code to fit your problem best (in Matlab or the language you prefer). Here it is a very good reference on the topic:
André Longtin: Stochastic delay-differential equations, in Fatihcan M. Atay (editor): Complex Time-Delay Systems. Theory and Applications, Springer 2010.
Numerical tools for solving Stochastic Differential Equations (SDE) can be found in the monograph of P.E. Kloeden and E. Platen: "Numerical Solution of Stochastic Differential Equations", Stochastic Modelling and Applied Probability, Springer, 1992/2011: Using the method of steps and applying these methods (like Euler-Maruyama as suggested above or higher order schemes as, e.g., the Milstein scheme) could help.
Nonetheless, there are already some particular numerical methods available for stochastic DDE - see, e.g.:
http://www.mathematik.hu-berlin.de/~buckwar/prepsmsm.pdf
http://ideas.repec.org/p/zbw/sfb373/199925.html
http://ideas.repec.org/p/zbw/sfb373/200130.html
I remember that to integrate when there is a delay, one has to consider that a given state at t is perturbed by past states included the interval from t to t-tau, tau your delay, not only by a single past state at t-tau. This I understood makes the state space infinite dimensional in the continuous case, in numerics it means one need to get (save them inject) the discretized past values belonging to the interval.
I tried to find that and no way, It is required to construct your own code.
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