How to keep track of markings in a Petri net

I am writing some code for a class assignment that determines the reachable states for a petri net. The net is fully conservative so there are no dominant nodes, but there may be repeats. I have come up with some basic code that determines the next states based on a given state.(See below) Now I am trying to figure out how to keep track of the paths (the tree)

Any advice or tips?

      Thanks!
%B (Incident Matrix) of plant and controller

%M0 is initial condition

%initial values

p=0; Mk=zeros(12,1);M=zeros(12,1);

% This loop tests each transition, and adds to list if fireable

for k=1:1:12

    Mk=M0+Bc(:,k);% Mk is M0 + kth column of Bc
    C=(Mk>=0); %C is test vector, returns 1 for elements >=0
    if(all(C)) % if all elements in Mk are non-neg
        p=p+1; %increment p
        M(:,p)=Mk; %Add to the Marking List
    end
end
M %display M