Hi Tuffers,
Indeed, finding life from a different tree would be phenomenal. As it stands, all life that we know of and have investigated thoroughly originates from a single tree. Everything uses the same set of codons (with minor modifications), hence everything is built using the same "language", and can be said to be derived from the same pool of ancestors.
There are a number of possible alternative biochemistries that may have existed on the early earth, including alternative genetic materials (see the PNA- peptide nucleic acid- world, or TNA- threose nucleic acid- world), alternatives to the A, U/T, G, and C nucleobases, and alternatives to phosphates (arsenate- see Wolfe-Simon et al., International Journal of Astrobiology, 2009). However, our current biochemistry seems to be the most robust, hence evolutionary pressure would have selected us.
That's not to say that other biochemistries don't exist out there. Some "shadow life", like NosyNed highlights, would be hard to detect. Those forms of shadow life may use alternative handedness to their biomolecules, may use a different set of codons, or may even go more weird than that. Unfortunately, most of biological equipment is practical in nature, and hence tailored to understanding "typical" biochemistry, so searches for alternative life are quite limited.