Unable to get the ARN for AWS SQS and its dead letter queue

Question

I am creating a sqs with a dead letter queue. The creation of the queue is success but I need to store the ARN value of the queue in systems manager at parameter store. Is there any way to pass the value to parameter store? Please provide inputs.

I tried like this, but it is not deploying in the parameter store.. I am deploying through cdk using python.

    dead_letter_queue: sqs.Queue = sqs.Queue(
        self,
        id="DeadLetterQueue",
        queue_name="dlqueue",
        retention_period=Duration.days(14)
    )
    self.sqs_queue: sqs.Queue = sqs.Queue(
        self,
        id="SqsQueue",
        queue_name="queue",
        retention_period=Duration.days(4),
        visibility_timeout=Duration.hours(6),
        delivery_delay=Duration.seconds(0),
        receive_message_wait_time=Duration.seconds(0),
        max_message_size_bytes=262144,  # 256 KiB
        #encryption=sqs.QueueEncryption.SQS_MANAGED,
        dead_letter_queue=sqs.DeadLetterQueue(
            max_receive_count=1,
            queue=dead_letter_queue

        )

    )

    ssm.StringParameter(self, "arn value of queue",
                        parameter_name="test",
                        string_value=self.sqs_queue.queue_arn)