Perhaps the easiest way to answer your poem would be to lead you in the direction of Metaphoric poetry. Metaphor poems are poems which use either simple metaphors to compare two typically unlike things or are compounded metaphors where the entire poem exists as a metaphor for something else.
One example of a metaphor poem is "The Garden Hose" by Beatrice Janosco:
In the grey evening
I see a long green serpent
With its tail in the dahlias
It lies in loops across the grass
And drinks softly at the faucet.
I can hear it swallow.
Here, Janosco is comparing a garden hose to a snake. Therefore, the poem contains a multiple meaning when looking at the poem with and without the title.
As for poetry which contains polysemy (characterized when a word alone has multiple meanings), this is a little more difficult. Given that poetry interpretation is typically left to the reader, many readers may not agree on the meaning of an entire poem or of the use of a word within the text of a poem.
To give you one example of this, examine the poem "The Waste Land" by T.S.Elliot:
I have heard the key
Turn in the door once and turn once only
We think of the key, each in his prison
Thinking of the key, each confirms a prison
The key spoken of in the excerpt of the poem can hold two very distinctive meanings.
First, the key can represent an actual key which releases one from an actual prison.
Second, the key can represent a metaphorical key which all must find in order to release them from a mental or emotional prison which they exist within.
I hope that this answers your question. Again, it is very hard to pinpoint polysemy in a specific poem because of personal interpretation.