\startuseMPgraphic{CountFrame}
  picture p; numeric w, h, o;
  p := textext.rt("\wrappedcurrentconstruction");
  w := OverlayWidth;
  h := OverlayHeight;
  o := BodyFontSize;
  p := p shifted (2o,h-ypart center p);
  draw p;
  path b;
  b := boundingbox p enlarged (o/10);
  path a;
  a := (2o,h)--(0,h)--(0,0)--(w,0)--(w,h)--(xpart urcorner b,h);
  drawoptions (withpen pencircle scaled 1pt withcolor black);
  draw a;
  draw b;
  setbounds currentpicture to OverlayBox;
\stopuseMPgraphic

\defineoverlay
  [CountFrame]
  [\useMPgraphic{CountFrame}]

\defineframedtext
  [CountFramedText]
  [frame=off,
   background=CountFrame,
   offset=\bodyfontsize,
   width=\textwidth,
%  style={\switchtobodyfont[11pt,tt]}]
   bodyfont=11pt,
   style={\tt}]

\defineenumeration
  [Code]
  [title=yes,
   alternative=empty,
   before=\startCountFramedText,
   after=\stopCountFramedText,
   left={\somenamedheadnumber{chapter}{current}.}]

\starttext

\startchapter
  [title=first]

\startCode
  [title={The First Title},
   reference={tit1}]
   Some verbatim text
\stopCode

\startCode
  [title={The Second Title},
   reference={tit2}]
   Some verbatim text
\stopCode

Refer to \in{code fragment}[tit1] bla

\stopchapter

\startchapter
  [title=second]

\startCode
  [title={The Third Title},
   reference={tit3}]
   Some verbatim text
\stopCode

\stopchapter

\stoptext