May I suggest an illustrative example which should guide you in the beginning ?
As noted you can't obtain any results using the given DNA sequence as it is. Instead you should transform it and what more natural than assigning integer values to each nucleobase ?
data = {A, C, G, T, A, C, G, T, A, C, C, C, C, A, G, G, G, A, T, T, T} /.
{A -> 1, G -> 2, T -> 3, C -> 4};
cwd = ContinuousWaveletTransform[data, GaborWavelet[]]
WaveletScalogram[cwd, ImageSize -> 500, ColorFunction -> "DeepSeaColors"]

Or if you need a finer resolution
ListDensityPlot[Abs@Reverse@cwd[All, "Values"], ColorFunction -> "DeepSeaColors"]

You can always observe the scalogram in 3D
f = cwd["LinearScalogramFunction"]
(* Real Part *)
Plot3D[Re@f[x, y], {x, 1., 21.}, {y, 1.15117, 7.74411}, ImageSize -> 500,
ColorFunction -> "SunsetColors"]

(* Imaginary part *)
Plot3D[Im@f[x, y], {x, 1., 21.}, {y, 1.15117, 7.74411}, ImageSize -> 500,
ColorFunction -> "SunsetColors"]

I will leave the interpretation of the scalograms to you.