What to do?
Since you have already learnt how mature is your GPIS, what are its strengths and weaknesses, you can start thinking about its improvement. The natural direction of development is achieving consecutive levels of GPM3. But GPIS improvements cannot be done within a few months; usually this process is spread over a few years.
Your government usually has specific priorities. Perhaps it pays special attention to infrastructural projects, maybe to projects restructuring its administration, maybe to IT projects or to other types of projects. Various factors may affect the fact that particular importance should be attached to cost management, project portfolio management, good specification of project products, cooperation with stakeholders or other project management areas.
Priorities, current GPIS maturity, situation, strengths, weaknesses and other factors (like culture) may be the basis for determining the roadmap for GPIS development in your country. You may choose any area for improvement like cost management, stakeholder engagement or, say, program management. These activities make up a program of project management improvement. Within a plan of such program you should document, among others, expected benefits, needed authorizations, funds, stakeholder engagement, timeline, and probably other factors specific to your government.