Is the following algebra 1-syzygy finite?

$Lambda$ is a finite dimensional algebra given by
$$xymatrix{1bulletar@<1ex>(rr)^{theta}ar@<-1ex>(rr)^{gamma}&&2bulletar@(r,d)()^{alpha}
&&&&{rm with} alpha^{3}=0}$$

Is $Lambda$ is 1-syzygy finite?