How about in the SQSResponse object

moto/sqs/models.py

@@ -121,7 +121,6 @@ class Queue(object):
         self.created_timestamp = now
         self.delay_seconds = 0
         self.last_modified_timestamp = now
-        self.maximum_message_size = 64 << 10
         self.message_retention_period = 86400 * 4  # four days
         self.queue_arn = 'arn:aws:sqs:sqs.us-east-1:123456789012:%s' % self.name
         self.receive_message_wait_time_seconds = 0
@@ -190,9 +189,6 @@ class Queue(object):
         return [message for message in self._messages if message.visible and not message.delayed]
 
     def add_message(self, message):
-        if len(message.body) > self.maximum_message_size:
-            raise InvalidParameterValue()
-
         self._messages.append(message)
 
     def get_cfn_attribute(self, attribute_name):

moto/sqs/responses.py

@@ -11,6 +11,7 @@ from .exceptions import (
 )
 
 MAXIMUM_VISIBILTY_TIMEOUT = 43200
+MAXIMUM_MESSAGE_LENGTH = 262144  # 256 KiB
 DEFAULT_RECEIVED_MESSAGES = 1
 SQS_REGION_REGEX = r'://(.+?)\.queue\.amazonaws\.com'
 
@@ -106,6 +107,9 @@ class SQSResponse(BaseResponse):
         message = self.querystring.get("MessageBody")[0]
         delay_seconds = self.querystring.get('DelaySeconds')
 
+        if len(message) > MAXIMUM_MESSAGE_LENGTH:
+            return "One or more parameters are invalid. Reason: Message must be shorter than 262144 bytes.", dict(status=400)
+
         if delay_seconds:
             delay_seconds = int(delay_seconds[0])
         else: