  In the present paper, we shall study the 4-dimensional Z_2 lattice gauge
model with a random gauge coupling; the random-plaquette gauge model(RPGM). The
random gauge coupling at each plaquette takes the value J with the probability
1-p and -J with p. This model exhibits a confinement-Higgs phase transition. We
numerically obtain a phase boundary curve in the (p-T)-plane where T is the
"temperature" measured in unit of J/k_B. This model plays an important role in
estimating the accuracy threshold of a quantum memory of a toric code. In this
paper, we are mainly interested in its "self-duality" aspect, and the
relationship with the random-bond Ising model(RBIM) in 2-dimensions. The
"self-duality" argument can be applied both for RPGM and RBIM, giving the same
duality equations, hence predicting the same phase boundary. The phase boundary
curve obtained by our numerical simulation almost coincides with this predicted
phase boundary at the high-temperature region. The phase transition is of first
order for relatively small values of p < 0.08, but becomes of second order for
larger p. The value of p at the intersection of the phase boundary curve and
the Nishimori line is regarded as the accuracy threshold of errors in a toric
quantum memory. It is estimated as p=0.110\pm0.002, which is very close to the
value conjectured by Takeda and Nishimori through the "self-duality" argument.
