Particolar solutions to a 4-variables diophantine equation

Question

Studying a certain problem, I came across the Diophantine equation $x^2 + y^2 + z^2 = 3t^2$. How can I find the solutions to the latter with the further condition that $(x,y,z,t)$ are pairwise coprime? I know that they must be all odds, and that $t$ is the only one that can be a multiple of 3. Do they have other properties? Obviously it admits solutions, such as the trivial $(1,1,1,1)$. Thanks in advance.