  Let k=F_q be a finite field of even characteristic. We obtain in this paper a
complete classification, up to k-isomorphism, of non singular quartic plane
curves defined over k. We find explicit rational normal models and we give
closed formulas for the total number of k-isomorphism classes. We deduce from
these computations the number of k-rational points of the different strata by
the Newton polygon of the non hyperelliptic locus M_3^{nh} of the moduli space
M_3 of curves of genus 3. By adding to these computations the knowed results on
the hyperelliptic locus we obtain a complete picture of these strata for M_3.
