dg.differential geometry - Deriving symmetries of a Gauge theory

Hello,
I don't know if this is a good place for exposing my problem but I'll try...

I have a gauge theory with action:

$S=int;dt L=int d^4 x ;epsilon^{munurhosigma} B_{munu;IJ} F_{munu}^{;;IJ} $

Where $B$ is an antisymmetric tensor of rank two and $F$ is the curvature of a connection $A$ i.e: $F=dA+Awedge A$, $mu,nu...$ are space-time indices and $I,J...$ are Lie Algebra indices (internal indices) I would like to find its symmetries. So I rewrite the Lagrangian by splitting time and space indices ${mu,nu...=0..3}equiv {O; i,j,...=1..3}$ I find:

$L = int d^3 x;(P^i_{;IJ}dot{A}_i+B_i^{,IJ}Pi^i_{,IJ}+A_0^{;IJ}Pi_{IJ})$

Where $dot{A}_i = partial_0 A_i$, $P^i_{;IJ} = 2epsilon^{ijk}B_{jk,IJ}$ is hence the conjugate momentum of $A_i^{,IJ}$

$B_i^{,IJ}$ and $A_0^{;IJ}$ being Lagrange multipliers we obtain respectively two primary and two secondary constraints:

$Phi_{IJ} = P^0_{;IJ} approx0$

$Phi_{;;IJ}^{munu} = P^{munu}_{;;IJ} approx0$

$Pi^i_{,IJ} = 2epsilon^{ijk}F_{jk,IJ} approx0$

$Pi_{IJ}=(D_i P^i)_{IJ} approx0$

Where $P^0_{;IJ}$ are the conjugate momentums of $A_0^{,IJ}$ and $P^{munu}_{;;IJ}$ those of $B_{munu}^{;;IJ}$. Making these constraints constant in time produces no further constraints.

Whiche gives us a general constraint:

$Phi = int d^3 x ;(epsilon^{IJ}P^0_{,IJ}+epsilon_{munu}^{IJ};P^{munu}_{;;IJ}+eta^{IJ}Pi_{IJ}+eta_i^{IJ}Pi^i_{;IJ})$

Each quantity $F$ have thus a Gauge transformation $delta F = {F,Phi}$ where ${...}$ denotes the Poisson bracket.

Knowing that this theory have the following Gauge symmetry:

$delta A = Domega$

$delta B = [B,omega]$

Where $omega$ is a 0-form, I would like to retrieve these transformations using the relation below. (where $Phi$ is considered as the generator of the Gauge symmetry) but my problem is that I don't know how to proceed, I already did this with a Yang-Mills theory and it worked... but for this theory it seems to le intractable! Someone to guide me?