It's impossible.

Concentrate on one of the corners of the square. There are two orientations of the z tetromino (assuming no reflection), and only one of these orientations can fill the corner, shown below.

Now note that in the valid configuration, the square marked 'A' is impossible to fill. Therefore, the 8x8 grid can't be tiled.

It is still impossible with reflections allowed. See figure below showing the top three rows of the 8x8 square.

The red tetromino is placed without loss of generality (from the argument above, rotations/reflections won't help). The only way to cover the cell marked 'B' is with the yellow tetromino, and similarly for the orange tetromino over 'C'. It is then impossible to fill cell 'D'.

If reflections are not allowed:

It's impossible.

The figures below show why.

Concentrate on one of the corners of the square. There are two orientations of the z tetromino (assuming no reflection), and only one of these orientations can fill the corner, shown below. 



Now note that in the valid configuration, the square marked 'A' is impossible to fill. Therefore, the 8x8 grid can't be tiled.

If reflections are allowed:

It is still impossible.

See figure below showing the top three rows of the 8x8 square.

The red tetromino is placed without loss of generality (from the argument above, rotations/reflections won't help). The only way to cover the cell marked 'B' is with the yellow tetromino, and similarly for the orange tetromino over 'C'. It is then impossible to fill cell 'D'.

It's impossible.

Concentrate on one of the corners of the square. There are two orientations of the z tetromino (assuming no reflection), and only one of these orientations can fill the corner, shown below.

Now note that in the valid configuration, the square marked 'A' is impossible to fill. Therefore, the 8x8 grid can't be tiled.

It's impossible.

Concentrate on one of the corners of the square. There are two orientations of the z tetromino (assuming no reflection), and only one of these orientations can fill the corner, shown below.

Now note that in the valid configuration, the square marked 'A' is impossible to fill. Therefore, the 8x8 grid can't be tiled.

It is still impossible with reflections allowed. See figure below showing the top three rows of the 8x8 square.

The red tetromino is placed without loss of generality (from the argument above, rotations/reflections won't help). The only way to cover the cell marked 'B' is with the yellow tetromino, and similarly for the orange tetromino over 'C'. It is then impossible to fill cell 'D'.