Im thinking it would be (E0*0*EUE1*E)? where E is the set of my alphabet, with at least 2 0s and at least 1 1
Try this expression:
^(.*0.*0.*1.*)|(.*0.*1.*0.*)|(.*1.*0.*0.*)$
EDIT Could be simplified to:
^.*(0.*0.*1)|(0.*1.*0)|(1.*0.*0).*$