I have no experience with Picard Java API (only the tools) but if this is not compulsory to use Picard & Java you could use bamtools C++ API to parse the whole BAM file and retrieve the information you want. Here follows a sample code to parse the BAM file, and where you can add your own specific processing:

//let's call this file do_bam.cpp

#include <iostream>
#include "api/BamReader.h"
#include "api/BamWriter.h"

using namespace std;
using namespace BamTools;

int main(int argc, char* argv[])
{
    string  inputFileName;

    if ( argc == 2 ) 
    {
            inputFileName  = argv[1] ;
    }
    else {
        cerr << "Wrong number of arguments." << endl;
        return 1;
    }

    BamReader reader;
    if (!reader.Open(inputFileName)) {
        cerr << "Could not open input BAM file." << endl;
        return 1;
    }

    BamAlignment al;
    while (reader.GetNextAlignment(al)) {

        // Add your own processing here
        // to get the desired information

    }

reader.Close();
return 0;
}

Compile with :

c++ -I /path/to/bamtools/include/ -L /path/to/bamtools/lib/ -o do_bam do_bam.cpp -lz -lbamtools

Documentation of BamTools API classes :

• http://pezmaster31.github.com/bamtools/index.html

Beside this, you may need a bed file with the genomic intervals of your genes of interest.

import java.io.File;
import net.sf.samtools.SAMFileReader;
import net.sf.samtools.SAMFileWriter;
import net.sf.samtools.SAMFileWriterFactory;
import net.sf.samtools.SAMRecord;
import net.sf.samtools.SAMRecordIterator;
import net.sf.samtools.SAMFileReader.ValidationStringency;

public class Biostar13454 {

static java.util.List<YourClassGene> my_list_of_genes;

public static void main(String[] args) throws Exception
    {
    if(args.length!=1) return;
    //init  my_list_of_genes ...
    SAMFileReader inputSam=new SAMFileReader(new File(args[0]));
    inputSam.setValidationStringency(ValidationStringency.SILENT);
    SAMRecordIterator iter=inputSam.iterator();

    while(iter.hasNext())
        {
        SAMRecord rec=iter.next();
        if(rec.getReadUnmappedFlag()) continue;
        for(YourClassGene g: my_list_of_genes)
           {
           if(!(rec.getReferenceName().equals(g.chromosome) && g.contains(rec.getAlignmentStart(),rec.getAlignmentStart())) continue;
           //do something
           }
        }
    iter.close();
    inputSam.close();
    }
 }

"I have only to get the name and the total reads values from each gene to do some calculus with it."

Sounds like you might just want to do something simple - get count of reads for each gene from a bam file?

If I interpreted your question correctly, read about coverageBed from bedtools, it will take a bam file and a bed file of genes and give you count of reads on each gene.