Once upon a time I thought about this a lot. I incorporated this poem into an article and used a version based on the one in Walter Vickery's book on Pushkin, except I altered it - and I can't recall if the first line was his version, or mine. I think he has the other word order: "I've raised a monument".

In any event, here's what I wrote about "нерукотворный", including a footnote to an entire article on the topic. Evidently Pushkin only used this word one time.



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Note added at 27 mins (2013-03-01 23:03:36 GMT)
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My thoughts: A few months before he was killed, Pushkin wrote his version of the Horatian ode on the immortality of the poet, “Exegi monumentum aere perennius. . .” (“I have built a monument more lasting than bronze . . .”). Derzhavin had begun his own ode on this theme:

Я памятник воздвиг чудесный, вечный...
A monument I’ve built, wondrous, eternal . . .

Keeping Derzhavin’s language exactly, through vozdvig, Pushkin then said something entirely new:

Я памятник воздвиг нерукотворный...
A monument I’ve built, unmanufactured . . .

Literally: “not by hands made.” Pushkin used the word nerukotvorny only this once. It is rooted in the Old Church Slavonic of the Gospels, where Jesus is reported to say he will build a new temple “without hands” (Mark, 14:58). In Russian, the term also describes miraculous icons, religious images believed to have been painted not with a brush in a human hand, but by divine intervention. [Note 50] The entire poem reads:

A monument I’ve raised that never hands could build,
The people’s path to it will not be overgrown,
Its head, unbowed, untamed, stands higher from the ground
Than Alexander’s column stands. [Etc.]

Note 50: David G. Huntley, “On the source of Pushkin’s nerukotvornyj,” Die Welt der Slaven (Wiesbaden, 1970), Jg. 15, Heft 4, p. 362.

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I don't find Huntley's article online. I guess I found it at the Library of Congress in olden times.

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Note added at 30 mins (2013-03-01 23:06:53 GMT)
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But if your sinister aim is not to translate the poem, but just to say something like that, then there would be several ways to play around with expressions alluding to St. Mark. Here's that verse:

We hear him say, I will destroy this temple that is made with hands, and within three days I will build another made without hands.

"made without hands"
"made by no man's hand"
etc.

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Note added at 31 mins (2013-03-01 23:07:26 GMT)
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Correction: We heard him say...

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Note added at 3 hrs (2013-03-02 02:22:36 GMT)
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See the poems I posted in the discussion. I think that if you're writing in English, you might do well to use some allusion to the classical English expressions of the same idea (and they both allude to Horace, of course), rather than Pushkin's - which indeed would tend not to be recognized.