The article is about irreducible representations of the convolution algebra \(M(\mathbb{H}_n)\) of bounded regular Borel measures on the unimodular Heisenberg group \(\mathbb{H}_n= \mathbb{C}^n\times \mathbb{R}\) for which the group structure is given by \[ (a,t)(b,s)= \left(a+b, s+t+\text{Im}{b-a\over 2} \right). \] A representation of \(\mathbb{H}_n\) on \(L^2(\mathbb{C}^n,d\mu)\) with \(d\mu(z)= {1 \over (2\pi)^n} \exp(-{| z|^2 \over 2})dz\) is defined by \(\rho(a,t) =e^{it} W_a\), where \[ (W_af)(z)=\exp \left({z.a \over 2}- {| a|^2 \over 4}\right) f(z-a). \] It is cut down to \(L^1(\mathbb{C}^n)\) and \(M(\mathbb{C}^n)\) via \(\widetilde \rho(\sigma)= \int_{\mathbb{C}^n} W_ad\sigma (a)\); \(M(\mathbb{H}_n)\) is a Banach algebra and on \(M(\mathbb{C}^n)\) a twisted convolution is considered given by \[ \int_{\mathbb{C}^n} \varphi(a)d(\tau\sharp \sigma)(a)= \int_{\mathbb{C}^n} \int_{ \mathbb{C}^n} \varphi(a+b) \exp(i\text{Im}(z.a)) d\tau(a)d \sigma(b). \] To the continuous bounded function \(\varphi\) on \(\mathbb{C}^n\) the Berezin-Toeplitz operator defined by \[ (T_\varphi f)(z)=\int_{\mathbb{C}^n}\varphi(a)f(a)e^{z.a\over 2}d\mu (a) \] is associated, where \(f\in L^2(\mathbb{C}^n,d\mu)\). The main result says that the operator norm closure of the set of \(T_\varphi\)'s coincides with the \(\mathbb{C}^*\)-algebra generated by \(\widetilde\rho\) on \(M(\mathbb{C}^n)_\sharp\) and the \(\mathbb{C}^*\)-algebra generated by \(\rho\) on \(M(\mathbb{H}^n)\).