N.M. Stat. § 17-4-12
Any person having already established or desiring to establish or maintain a park or lake for the purpose of keeping or propagating and selling the game or game fish therein or to be placed therein, shall apply in writing to the warden [director of the department of game and fish] stating the name, location, extent and proprietorship of the same, and kind and as near as may be, the number of game or game fish kept or desired to be kept therein, the term for which the license is desired and inclosing the fee therefor, and if upon examination by the warden it shall appear that the application is in good faith, and in other respects proper and reasonable, he shall grant to such applicant a license therefor; provided that the maximum area that may be included within any park shall not exceed three thousand two hundred acres, and that every park shall be enclosed by a game proof fence which shall conform to specifications required by the state game commission.
NMS § 17-4-12