Combining vlookup with offset?

I've been trying to automate a process whereby I transfer data from one worksheet to another in the same workbook.

The original sheet has the data in the form of matrices, where, on the first row, there is a unique code specific to each matrix. Here's an example, with the unique code coloured red:

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On the second worksheet, the data has to be transformed to look like this:

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Where the data from the matrices are converted into columns.

I'd like to be able to place the codes for the matrices into the first row of the second sheet, then search for that code in the first sheet, then using that cell as a reference, automatically return the data in columnar format.

Does that make sense?

I know how to use VLOOKUP to search for a unique code in a column, and I know how to use OFFSET to transform the data, by referring to a single cell. But I can't for the life of me figure out how to combine the two.

Please help me avoid a meltdown!

Undoubtedly you can do this with formulae but I find it easier using code. I post this in case it's of use, which assumes the blocks have five columns.

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(The unique code appears in Column B of Sheet 3, if that was not obvious)

Well if it works then I'd say there's nothing wrong with it. That's not to say that one of the formula experts wouldn't be able to shorten it considerably. Did you try the code?