In this paper we present LXGram, a general purpose grammar for the deep linguistic processing of Portuguese that aims at delivering detailed and high precision meaning representations. LXGram is grounded on the linguistic framework of Head-Driven Phrase Structure Grammar (HPSG). HPSG is a declarative formalism resorting to unification and a type system with multiple inheritance. The semantic representations that LXGram associates with linguistic expressions use the Minimal Recursion Semantics (MRS) format, which allows for the underspecification of scope effects. LXGram is developed in the Linguistic Knowledge Builder (LKB) system, a grammar development environment that provides debugging tools and efficient algorithms for parsing and generation. The implementation of LXGram has focused on the structure of Noun Phrases, and LXGram accounts for many NP related phenomena. Its coverage continues to be increased with new phenomena, and there is active work on extending the grammar's lexicon. We have already integrated, or plan to integrate, LXGram in a few applications, namely paraphrasing, treebanking and language variant detection. Grammar coverage has been tested on newspaper text.