Here is a code in Macaulay2 for checking that some plurisubharmonic function determines a contact structure
R = QQ[x,y,z,t]
degf=4
f=x^degf+y^degf+z^degf+t^degf + 3x^2z^2 + x^2*t^2
--f2 = x^degf+y^degf+z^degf+t^degf
nR = diff(y,f)*x-diff(x,f)*y+diff(t,f)*z-diff(z,f)*t
cdx = degffdiff(y,f)-nR*diff(x,f)
cdy = -degffdiff(x,f)-nR*diff(y,f)
cdz = degffdiff(t,f)-nR*diff(z,f)
cdt = -degffdiff(z,f)-nR*diff(t,f)
cxyz=cdx*(diff(y,cdz)-diff(z,cdy))+cdy*(diff(z,cdx)-diff(x,cdz))+cdz*(diff(x,cdy)-diff(y,cdx))
re = sub(cxyz,t=>1)
factor re
So, $f2=x^4+y^4+z^4+t^4\ $ (in the above notation) does NOT produce contact structure. It is convex but not strictly(!) plurisubharmonic (on the plane $x=y=0$). Here (http://www.math.ethz.ch/~evansj/lecture9.pdf) there is a good explanation why the induced structure is contact ($d\eta$ tames complex structure on $\mathbb R^4$ )