If the trans thats currently mounted on the engine is the original, the engine by simple deduction, the engine is going to be from a HD pickup truck as thats the only application that used this manual trans. The Duramax and the 8.1 engines came with the Allison Auto and the ZF S6-650 6 speed manual and only the LQ4 came with the NV4500.
From my post, if the LQ4 has iron heads, it a 99-2000 LQ4. If it has aluminum heads I can tell its a 2001-2007 LQ4. But the block casting number you supplied me only runs up to 2004 from what I can tell. So my educated guess is that you have a 2001-2004 LQ4 6.0 engine from a 2001-2004 3/4 ton or 1 ton truck.
the head code you supplied means nothing to me unfortunatley.
Why do you need the exact vehicle the engine came from if I may ask?