If you need to get Object Type Code of entity based on Logical Name of entity you can use following code:

var entityLogicalName = "account";

var requestUrl = "/api/data/v8.2/EntityDefinitions?$filter=LogicalName eq '" + entityLogicalName + "'&$select=ObjectTypeCode";

var context;

if (typeof GetGlobalContext === "function") {
    context = GetGlobalContext();
} else {
    context = Xrm.Page.context;
}
var req = new XMLHttpRequest();
req.open("GET", context.getClientUrl() + requestUrl, true);
req.setRequestHeader("OData-MaxVersion", "4.0");
req.setRequestHeader("OData-Version", "4.0");
req.setRequestHeader("Accept", "application/json");
req.setRequestHeader("Content-Type", "application/json; charset=utf-8");
req.onreadystatechange = function () {
    if (this.readyState === 4) {
        req.onreadystatechange = null;
        if (this.status === 200) {
            var result = JSON.parse(this.response);
            var objectTypeCode = result.value[0].ObjectTypeCode;
            //use retrieved objectTypeCode
        } else {
            var errorText = this.responseText;
            //handle error here
        }
    }
};
req.send();