You may either work with an extended building as L. Spice suggests in his answer, or consider the following based on the fact that a generalized $BN$-pair contains a genuine $BN$-pair. With you notation, the group $N$ writes as a semidirect product $\Omega\ltimes N_0$ for some invariant subgroup $N_0$ of $N$. Then $G_0 = BN_0 B$ is a group with a true $BN$-pair $(B,N_0 )$, and we have $G = \Omega \ltimes G_0$. We may form the building $X$ for $G_0$ with respect to the $BN$-pair $(B,N_0 )$. Recall that $X$ is a simplicial complex whose vertices are in $G_0$-equivariant bijection with the parahoric subgroups $P$ of $G_0$. The action of $G$ by conjugation permutes the parahoric subgroups of $G$, whence induces a simplicial action of $G$ on $X$.

You may either work with an extended building as L. Spice suggests in his answer, or consider the following based on the fact that a generalized $BN$-pair contains a genuine $BN$-pair. With you notation, the group $N$ writes as a semidirect product $\Omega\ltimes N_0$ for some invariant subgroup $N_0$ of $N$. Then $G_0 = BN_0 B$ is a group with a true $BN$-pair $(B,N_0 )$, and we have $G = \Omega \ltimes G_0$. We may form the building $X$ for $G_0$ with respect to the $BN$-pair $(B,N_0 )$. Recall that $X$ is a simplicial complex whose vertices are in $G_0$-equivariant bijection with the parahoric subgroups $P$ of $G_0$. The action of $G$ by conjugation permutes the parahoric subgroups of $G_0$, whence induces a simplicial action of $G$ on $X$.