  In terms of the creative microscoping method recently introduced by Guo and
Zudilin and the Chinese remainder theorem for coprime polynomials, we establish
a $q$-supercongruence with two parameters modulo $[n]\Phi_n(q)^3$. Here
$[n]=(1-q^n)/(1-q)$ and $\Phi_n(q)$ is the $n$-th cyclotomic polynomial in $q$.
In particular, we confirm a recent conjecture of Guo and give a complete
$q$-analogue of Long's supercongruence. The latter is also a generalization of
a recent $q$-supercongruence obtained by Guo and Schlosser.
