We present the first general search for new heavy particles, X, which decay via X --> WZ0 --> e(nu)+jj as a function of M(X) and Gamma(X) in pp collisions at square root[s] = 1.8 TeV. No evidence is found for production of X in 110 pb(-1) of data collected by the Collider Detector at Fermilab. General cross section limits are set at the 95% C.L. as a function of mass and width of the new particle. The results are further interpreted as mass limits on the production of new heavy charged vector bosons which decay via W' --> WZ0 in an extended gauge model as a function of the width, Gamma(W'), and mixing factor between the W' and the standard model W bosons.