Java enum containing a hash map for look up
Your code is very neat and clean, there is only one thing that I would change:

private static Map&lt;String, String&gt; mMap;


to

private static final Map&lt;String, String&gt; mMap = Collections.unmodifiableMap(initializeMapping());


The reasons:


By not declaring it final and not using a call to unmodifiableMap it is mutable, and it would be possible to modify the reference using reflection or to use .remove("ABC") on the map. Declaring it as final makes sure that the referenced map cannot change and unmodifiableMap makes sure that no changes can be done to the map itself.
Multi-threading issues. As it currently stands, if two threads would call the getDescriptionByCode method at the same time you would initialize the mapping twice, which is not needed.


This also of course requires a slight change in your initializeMapping():

private static Map&lt;String, String&gt; initializeMapping() {
    Map&lt;String, String&gt; mMap = new HashMap&lt;String, String&gt;();
    for (Maps s : Maps.values()) {
        mMap.put(s.code, s.description);
    }
    return mMap;
}


Besides this, it all looks good. Well done!