I am trying to construct a field with 27 elements, and find a primitive element in that field. I considered the irreducible polynomial $f(x)=x^3+2x+1$ over $\mathbb{Z}\_3[x]$. Then I considered 
$$\mathbb{Z}\_3[x]/\langle f\rangle.$$
This is a field with $3^{\deg f}=3^3=27$ elements. I know that the unique elements of this field are given by 
$$\{a\_0+a\_1t+a\_2t^2:a\_i\in\mathbb{Z}\_3\}$$
where $t=x+\langle f\rangle$. Now my question is, what is an efficient way (for beginners) to find a primitive element of this field? One could argue that it suffices to find an element $u\in\mathbb{Z}\_3[x]/\langle f\rangle$ with $\text{ord}(u)\neq 1,2,13$, but finding such a $u$ is computationally tedious (at least to me). Any comments or advice appreciated.