Json.NET JSONPath query not returning expected results

I'm using Newtonsoft's Json.Net to select nodes from the following json:

{  
   "projects":[  
      {  
         "name":"Project 1",
         "client":{  
            "code":"ABC",
            "name":"Client 1"
         }
      },
      {  
         "name":"Project 2",
         "client":{  
            "code":"DEF",
            "name":"Client 2"
         }
      },
      {  
         "name":"Project 3",
         "client":{  
            "code":"GHI",
            "name":"Client 3"
         }
      }
   ]
}

The following c# snippet

//json is a JObject representation of the json listed above
var clients =  json.SelectTokens("$.projects[*].client");

Yields:

[  
   {  
      "code":"ABC",
      "name":"Client 1"
   },
   {  
      "code":"DEF",
      "name":"Client 2"
   },
   {  
      "code":"GHI",
      "name":"Client 3"
   }
]

Which is cool, now, what I'd like to do is filter by client code, I would think that

$.projects[*].client[?(@.code == 'DEF')]

would work, but I obviously don't understand the syntax well enough. This returns an empty list:

 var test1 =  json.SelectTokens("$.projects[*].client[?(@.code == 'DEF')]").ToList();

And the single token selector returns a null:

  var test2 =  json.SelectToken("$.projects[*].client[?(@.code == 'DEF')]");

I tried a few different configurations on https://jsonpath.curiousconcept.com/ and it seems my query syntax is indeed broken.

Using Flow Communications' JSONPath 0.3.4 implementation (on the above link) I can get the client using

$..[?(@.code == 'DEF')]

however, this syntax does not seem valid for Json.Net (nor the Goessner implementation on the same page).

Anyone see what I'm doing wrong?